# Programme And Abstracts For Wednesday 13^{th} Of December

Wednesday 13^{th} 10:30 098 Lecture Theatre (260-098)

## Promoting Your R Package

Hadley Wickham

RStudio

**Abstract:** Your new statistical or data science tool is much more likely to be used if you provide it in a convenient form, like an R package. But how do people find out that your R package exists? I’ll provide a comprehensive overview of the options, including creating excellent documentation (with roxygen2) and vignettes (with rmarkdown), creating a package website (with pkgdown), and promoting your work on social media.

**Keywords:**R packages, websites

Wednesday 13^{th} 10:30 OGGB4 (260-073)

## A Smoothing Filter Modelling Approach For Time Series

Marco Reale^{1}, Granville Tunnicliffe Wilson^{2}, and John Haywood^{3}

^{1}University of Canterbury

^{2}Lancaster University

^{3}Victoria University of Wellington

**Abstract:** We introduce different representations of a new model for time series based on repeated application of a filter to the original data. They can represent correlation structure to higher lags with fewer coefficients and they can provide a robust prediction at higher lead times.

**Keywords:**Time series, smooting, parsimonious models

Wednesday 13^{th} 10:30 OGGB5 (260-051)

## Online Learning For Bayesian Nonparametrics: Weakly Conjugate Approximation

Yongdai Kim^{1}, Kuhwan Jeong^{1}, Byungyup Kang^{2}, and Hyoju Chung^{2}

^{1}Seoul National University

^{2}NAVER Corp.

**Abstract:** We propose a new online learning method for Bayesian nonparametric (BNP) models so called *weakly conjugate approximation* (WCA). We consider classes of BNP priors which are weakly conjugate. Here, ‘weakly conjugate prior’ means that the resulting posterior can be easily approximated by an efficient MCMC algorithm.

Suppose the whole data set is divided into two groups, say \({{\bf x}}=({{\bf x}}^{old},{{\bf x}}^{new}).\) Then, the Bayes rule implies \(p(\theta|{{\bf x}}) \propto p({{\bf x}}^{new}|\theta) p(\theta|{{\bf x}}^{old}),\) where \(\theta\) is the parameter. WCA replaces \(p(\theta|{{\bf x}}^{old})\) with \(p^{wk}(\theta|\eta)\) where the proxy parameter \(\eta\) is estimated by minimizing the Kullback-Leibler (KL) divergence \({\mathbb{E}}_{p(\theta|{{\bf x}}^{old})}\left\{ \log p(\theta|{{\bf x}}^{old}) - \log p^{wk}(\theta|\eta)\right\}.\) It can be easily approximated when we can generate samples from \(p(\theta|{{\bf x}}^{old}).\) To be more specific, suppose \(\theta_1,\ldots,\theta_M\) are samples generated from \(p(\theta|{{\bf x}}^{old}).\) Then, we can estimate \(\eta\) by minimizing \(\sum_{j=1}^M\left\{ \log p(\theta_j|{{\bf x}}^{old}) - \log p^{wk}(\theta_j|\eta)\right\}/M.\)

To apply WCA for online learning with multiple batches, suppose the whole data \({{\bf x}}\) are divided into multiple small batches as \({{\bf x}}=({{\bf x}}^{[1]},\ldots,{{\bf x}}^{[S]}).\) A WCA algorithm sequentially approximates \(p(\theta|{{\bf x}}^{[1]},\ldots,{{\bf x}}^{[s]})\) by \(p^{wk}(\theta|\eta_s),\) where \(\eta_s\) is the proxy parameter minimizing the approximated KL divergence. Since \(p^{wk}(\theta|\eta)\) is weakly conjugate, we can easily generate samples from \(p({{\bf x}}^{[s]}|\theta)p^{wk}(\theta|\eta_{s-1}),\) and hence easily update \(\eta_s.\)

We compare several online learning algorithms by analyzing simulated/real data sets in Dirichlet process mixture models and hierarchical Dirichlet processes topic models. The proposed method shows better accuracy in our experiments.

**Keywords:**online learning, weakly conjugate approximation, Dirichlet process mixture model, hierarchical Dirichlet processes

Wednesday 13^{th} 10:30 Case Room 2 (260-057)

## Improving The Production Cycle At Stats NZ With RStudio

Gareth Minshall and Chris Hansen

Stats NZ

**Abstract:** Stats NZ are looking to move away from the collection and publication of stand-alone surveys to making use of a wide range of data sources and estimation strategies. A key component to enabling this change is to develop the infrastructure which allows analysts to explore, test and use a range of tools which are not traditionally heavily used within National Statistics Offices. One of the tools Stats NZ is looking to make heavier use of is R. This talk will outline the development of internal RStudio and Shiny servers at Stats NZ, and give examples demonstrating the types of innovation RStudio has enabled at Stats NZ to improve the way we produce and disseminate statistics.

**Keywords:** Shiny, R Markdown, Official Statistics

**Acknowledgement:**This work was supported by JSPS KAKENHI Grant Number JP16H02013.

Wednesday 13^{th} 10:30 Case Room 3 (260-055)

## A Max-Type Multivariate Two-Sample Baumgartner Statistic

Hidetoshi Murakami

Tokyo University of Science

**Abstract:** A multivariate two-sample testing problem is one of the most important topics in nonparametric statistics. Further, a max-type Baumgartner statistic based on the modified Baumgartner statistic (Murakami, 2006) was proposed by Murakami (2012) for testing the equality of two continuous distribution functions. In this paper, a max-type multivariate two-sample Baumgartner statistic is suggested based on the Jurečková and Kalina’s ranks of distances (Jurečková and Kalina, 2012). Simulations are used to investigate the power of the suggested statistic for various population distributions. The results indicate that the proposed test statistic is more suitable than various existing statistics for testing a shift in the location, scale and location-scale parameters.

**Keywords:** Baumgartner statistic, Jurečková & Kalina’s ranks of distances, Multivariate two-sample rank test, Power comparison

**References:**

Jurečková, J. and Kalina, J. (2012). Nonparametric multivariate rank tests and their unbiasedness. *Bernoulli*, **18**, 229–251.

Murakami, H. (2006). A \(k\)-sample rank test based on the modified Baumgartner statistic and its power comparison. *Journal of the Japanese Society of Computational Statistics*, **19**, 1–13.

*Journal of the Japanese Society of Computational Statistics*,

**25**, 39–49.

Wednesday 13^{th} 10:30 Case Room 4 (260-009)

## Random Search Global Optimization Using Random Forests

Blair Robertson, Chris Price, and Marco Reale

University of Canterbury

**Abstract:** The purpose of a global optimization algorithm is to efficiently find an objective function’s global minimum. In this talk we consider bound constrained global optimization, where the search is performed in a box, denoted \(\Omega\). The global optimization problem is deceptively simple and it is usually difficult to find the global minimum. One of the difficulties is that there is often no way to verify that a local minimum is indeed the global minimum. If the objective function is convex, the local minimum is also the global minimum. However, many optimization problems are not convex. Of particular interest in this talk are objective functions that lack any special properties such as continuity, smoothness, or a Lipschitz constant.

A random search algorithm for bound constrained global optimization is presented. This algorithm alternates between partition and sampling phases. At each iteration, points sampled from \(\Omega\) are classified low or high based on their objective function values. These classified points define training data that is used to partition \(\Omega\) into low and high regions using a random forest. The objective function is then evaluated at a number of points drawn from the low region and from \(\Omega\) itself. Drawing points from the low region focuses the search in areas where the objective function is known to be low. Sampling \(\Omega\) reduces the risk of missing the global minimum and is necessary to establish convergence. The new points are then added to the existing training data and the method repeats.

A preliminary simulation study showed that alternating between random forest partition and sampling phases was an effective strategy for solving a variety of global optimization test problems. The authors are currently refining the method and extending the set of test problems.

**Keywords:**Bound constrained optimization, classification and regression trees (CART), stochastic optimization

Wednesday 13^{th} 10:50 098 Lecture Theatre (260-098)

## gridSVG: Then And Now

Paul Murrell

University of Auckland

**Abstract:** The **gridSVG** package[@RJ-2014-013] was first developed in 2003 to experiment with features of the SVG format that were not available through a normal R graphics device[@R], such as hyperlinks and animation. A number of different R packages[@rsvgtipsdevice; @cairo; @svglite; @svgannotation] have been developed since then to allow the generation of SVG output from R, but **gridSVG** has remained unique in its focus on generating structured and labelled SVG output. The reason for that was to maximise support for customisation and reuse, particularly unforseen reuse, of the SVG output. Unfortunately, there were two major problems: killer examples of customisation and reuse failed to materialise; and the production of SVG with **gridSVG** was painfully slow. In brief, **gridSVG** was a (sluggish) solution waiting for a problem. This talk charts some of the developments over time that have seen **gridSVG**’s patient wait for relevance ultimately rewarded and its desperate need for speed finally satisfied.

**Keywords:**R, statistical graphics, SVG, accessibility

Wednesday 13^{th} 10:50 OGGB4 (260-073)

## Probabilistic Outlier Detection And Visualization Of Smart Meter Data

Rob Hyndman

Monash University

**Abstract:** It is always a good idea to plot your data before fitting any models, making any predictions, or drawing any conclusions. But how do you actually plot data on thousands of smart meters, each comprising thousands of observations over time? We cannot simply produce time plots of the demand recorded at each meter, due to the sheer volume of data involved.

I will propose an approach in which each long series of demand data is converted to a single two-dimensional point that can be plotted in a simple scatterplot. In that way, all the meters can be seen in the scatterplot; so outliers can be detected, clustering can be observed, and any other interesting structure can be examined. To illustrate, I will use data collected during a smart metering trial conducted by the Commission for Energy Regulation (CER) in Ireland.

First we estimate the demand percentiles for each half hour of the week, giving us 336 probability distributions per household. Then, we compute the distances between pairs of households using the sum of Jensen–Shannon distances.

From these pairwise distances, we can compute a measure of the “typicality” of a specific household, by seeing how many similar houses are nearby. If there are many households with similar probability distributions, the typicality measure will be high. But if there are few similar households, the typicality measure will be low. This gives us a way of finding anomalies in the data set — they are the smart meters corresponding to the least typical households.

The pairwise distances between households can also be used to create a plot of all households together. Each of the household distributions can be thought of as a vector in \(K\)-dimensional space where \(K=7\times48\times99 = 33,264\). To easily visualize these, we need to project them onto a two-dimensional space. I propose using Laplacian eigenmaps which attempt to preserve the smallest distances — so the most similar points in \(K\)-dimensional space are as close as possible in the two-dimensional space.

This way of plotting the data easily allows us to see the anomalies, to identify any clusters of observations in the data, and to examine any other structure that might exist.

Wednesday 13^{th} 10:50 OGGB5 (260-051)

## The Joint Models For Nonlinear Longitudinal And Time-To-Event Data Using Penalized Splines: A Bayesian Approach

Thi Thu Huong Pham, Darfiana Nur, and Alan Branford

Flinders University

**Abstract:** The joint models for longitudinal data and time-to-event data have been introduced to measure the association between longitudinal data and survival time in clinical, epidemiological and educational studies.. The main aim of this talk is to estimate the parameters in the joint models using a Bayesian approach for nonlinear longitudinal data and time-to-event data using penalized splines. To perform this analysis, the joint posterior distribution of hazard rate at baseline, survival and longitudinal coefficient and random effects parameters is first being introduced followed by derivation of the conditional posterior distributions for each of parameter. Based on these target posterior distributions, the samples of parameters are simulated using Metropolis, Metropolis Hastings and Gibbs sampler algorithms. An R program is written to implement the analysis. Finally, the prior sensitivity analysis for the baseline hazard rate and association parameters is performed following by simulations studies and a case study.

**Keywords:** Bayesian analysis, Joint models, Longitudinal data, MCMC algorithms, Prior sensitivity analysis, Survival data

**References:**

D. Rizopoulos, D. (2014). The R package JMbayes for fitting joint models for longitudinal and time-to- event data using MCMC. *Journal of Statistical Software,* 72(7):1 – 45.

*Biometrics,*61(1):64 – 73.

Wednesday 13^{th} 10:50 Case Room 2 (260-057)

## R – A Powerful Analysis Tool To Improve Official Statistics In Romania

Nicoleta Caragea^{1,2} and Antoniade Ciprian Alexandru^{1,2}

^{1}National Institute of Statistics

^{2}Ecological University of Bucharest

**Abstract:** This presentation is focused on how R is used in Romanian official statistics to improve the quality of results provided by different statistical data sources on the base of administrative data. Some benefits for statistical analysis come when it is possible to link administrative records from different registers together, or when they can be linked with censuses or sample surveys. Many of these record linkage or matching methods must be done under statistically conditions, R program being one of the most powerful analysis tool. In Romania, there has been increasing attention in recent years to use R in official statistics, through specialized R courses for statisticians and training on the job sessions. A international conference on R (uRos) is yearly organized to provide a public forum for researchers from academia and institutes of statistics. It is also a continuous work to develop statistics based on Big Data, Romania being part of the ESSnet Big Data Project.

**Keywords:**R package, data sources, statistics, matching method, linkage method

Wednesday 13^{th} 10:50 Case Room 3 (260-055)

## Simultaneous Test For Mean Vectors And Covariance Matrices In High-Dimensional Settings

Takahiro Nishiyama^{1} and Masashi Hyodo^{2}

^{1}Senshu University

^{2}Osaka Prefecture University

**Abstract:** Let \(\mathbf{X}_{g1}, \mathbf{X}_{g2}, \ldots, \mathbf{X}_{gn_g}\) be i.i.d. random samples of size \(n_g\) from a \(p\)-dimensional population \(\Pi_g\) (\(g \in \{1, 2\}\)) with \(\mathrm{E}(\mathbf{X}_{gi})={\boldsymbol\mu}_g\) and ${}({}_{gi})=_g$ (\(i \in \{1, \ldots ,n_g\}\)). In this talk, our primary interest is to test following hypothesis when \(p > \min\{n_1-1, n_2-1 \}\): \[\begin{aligned}
H_0 : {\boldsymbol\mu}_1 = {\boldsymbol\mu}_1,~ \Sigma_1 = \Sigma_2 \quad
\mbox{vs.} \quad H_1 : \mbox{not}~ H_0.
\end{aligned}\]

For this problem, we discuss an \(L^2\)-norm-based test for simultaneous testing of mean vectors and covariance matrices among two non-normal populations. To construct a test procedure, we propose a test statistic based on both unbiased estimator of differences mean vectors proposed by Chen and Qin (2010) and covariance matrices proposed by Li and Chen (2012). Also, we derive an asymptotic distribution of this test statistic and investigate the asymptotic sizes and powers of the proposed test. Finally, we study the finite sample and dimension performance of this test via Monte Carlo simulations.

**Keywords:** Asymptotic distribution, High-dimensional data analysis, Testing hypothesis

**References:**

Chen, S.X. and Qin, Y.L. (2010). A two-sample test for high dimensional data with applications to gene-set testing. *Ann. Statist.*, **38**, 808–835.

*Ann. Statist.*,

**40**, 908–940.

Wednesday 13^{th} 10:50 Case Room 4 (260-009)

## Dimension Reduction For Classification Of High-Dimensional Data By Stepwise SVM

Elizabeth Chou and Tzu-Wei Ko

National Chengchi University

**Abstract:** The purpose of this study is to build a simple and intuitive wrapper method, stepwise SVM, for reducing dimension and classification of large p small n datasets. The method employs a suboptimum search procedure to determine the best subset of variables for classification. The proposed method is compared with other dimension reduction methods, such as Pearson product moment correlation coefficient (PCCs), Recursive Feature Elimination based on Random Forest (RF-RFE), and Principal Component Analysis (PCA) by using five gene expression datasets. In this study, we show that stepwise SVM can effectively select the important variables and perform well in prediction. Moreover, the predictions of reduced datasets from stepwise SVM are better than that of the unreduced datasets. Compared with other methods, the performance of stepwise SVM is more stable than PCA and RF-RFE but it is difficult to tell the difference in performance from PCCs. In conclusion, stepwise SVM can effectively eliminate the noise in data and improve the prediction accuracy.

**Keywords:**Stepwise SVM, Dimension reduction, Feature selection, High-dimension

Wednesday 13^{th} 11:10 098 Lecture Theatre (260-098)

## Bringing Multimix From Fortran To R

Murray Jorgensen

Auckland University of Technology

**Abstract:** Multimix is the name for a class of multivariate finite mixture models designed with clustering (*unsupervised learning*) in mind. It is also a name for a program to fit these models, written in Fortran77 by Lyn Hunt as part of her Waikato PhD thesis.

**Why convert to R?** Although written in the 1990s Multimix is easy to convert to modern GNU Fortran (gfortran) but there are advantages to having an R version available. For users this means a simpler way of reading in the data and describing the form of the model. Also for ongoing development of improvement and modifications of the Multimix models. R’s interactive environment provides a more comfortable place for experimentation. Designing the new program. Rather than attempt any sort of translation of the old code, the new R version of Multimix is designed from the beginning as an R program. In my talk I will describe some of the design decisions made and the reasons for them. A particular concern was that the R version be as fast as possible.

**How to package up the new program?** Two versions of Multimix in R have been developed, a *global* version with many global variables employed, and a *nested* version restricting the scope of variables to the surrounding function. The pluses and minuses of each approach will be described. I am conscious that I may not always have made the best design decisions and comments from others will be welcomed.

**Keywords:**multivariate finite mixture models, clustering, package, global, local

Wednesday 13^{th} 11:10 OGGB4 (260-073)

## Specification Of GARCH Model Under Asymmetric Error Innovations

Oyebimpe Adeniji, Olarenwaju Shittu, and Kazeeem Adepoju

University of Ibadan

**Abstract:** An empirical analysis of the mean return and conditional variance of Nigeria Stock Exchange (NSE) index is performed using various error innovations in GARCH models. Conventional GARCH model which assumed normal error term failed to capture volatility clustering, leptokurtosis and leverage effect as a result of zero skewness and kurtosis respectively. We re-modify error distributions of GARCH (p,q) model inference using some thick-tailed distributions. Method of Quasi-Maximum Likelihood Estimation (MLE) was used in parameter estimation. The robust model that explained the NSE index is determined by loglikelihood and model selection Criteria. Our result shows that GARCH model with fat-tailed densities improves overall estimation for measuring conditional variance. The GARCH model using Beta-Skewed-t distribution is the most successful for forecasting NSE index.

**Keywords:**GARCH, Nigeria stock index, Maximum Lilkelihood Estimation (MLE), Beta Skewed -t distributions

Wednesday 13^{th} 11:10 OGGB5 (260-051)

## Performance Of Bayesian Credible Interval For Binomial Proportion Using Logit Transformation

Toru Ogura^{1} and Takemi Yanagimoto^{2}

^{1}Mie University Hospital

^{2}Institute of Statistical Mathematics

**Abstract:** The confidence or the credible interval of the binomial proportion \(p\) is one of most widely employed statistical analysis methods, and a variety of methods have been proposed. The Bayesian credible interval attracts recent researches’ attentions. One of the promising methods is the highest posterior density (HPD) interval, which implies the shortest possible interval enclosing \(100(1-\alpha)\)% of the probability density function. The HPD interval is often used because it is narrow compared to other credible intervals. However, the HPD interval has some drawbacks when the binomial proportion is a small. To dissolve them, we calculate first a credible interval by the HPD interval of the logit transformed parameter, \(\theta=\log\{p/(1-p)\}\), instead of \(p\). Note that \(\theta\) and \(p\) are the canonical and the mean parameters of the binomial distribution in the exponential family, respectively. Writing the HPD interval of \(\theta\) as \((\theta_{l}, \theta_{u})\), we define the proposed credible interval of \(p\) as \((p_{l}, p_{u})= \big( e^{\theta_{l}} / ( 1+e^{\theta_{l}} ), \, e^{\theta_{u}}/(1+e^{\theta_{u}}) \big)\). It is explored in depth, and numerical comparison studies are conducted to confirm its favorable performance, especially when the observed number is small, such as 0 or 1. Practical datasets are analyzed to examine the potential usefulness for applications in medical fields.

**Keywords:** Bayesian credible interval, binomial proportion, highest posterior density interval, logit transformation, zero count

**References:**

*Confidence Intervals for Proportions and Related Measures of Effect Size*. Florida: Chapman and Hall/CRC.

Wednesday 13^{th} 11:10 Case Room 2 (260-057)

## Statistical Disclosure Control With R: Traditional Methods And Synthetic Data

Matthias Templ

Zurich University of Applied Sciences

**Abstract:** The demand for and volume of data from surveys, registers or other sources containing sensible information on persons or enterprises have increased significantly over the last several years. At the same time, privacy protection principles and regulations have imposed restrictions on the access and use of individual data. Proper and secure microdata dissemination calls for the application of statistical disclosure control methods to the data before release. Traditional approaches to (micro)data anonymization, including data perturbation methods, disclosure risk methods, data utility and methods for simulating synthetic data have been made available in R. After introducing the audience to the R packages sdcMicro and simPop, the presentation will focus on new developments and research for generating close-to-reality synthetic data sets using specific model-based approaches. The resulting data can work as a proxy of real-world data and they are useful for training purposes, agent-based and/or microsimulation experiments, remote execution as well as they can be provided as public-use files. The strength and weakness of the methods are highlighted and an (brief) application to the Euorpean Statistics of Income and Living Condition Survey is given.

**Keywords:** Statistical Disclosure Control, Anonymization, Disclosure Risk, Synthetic Data

**References:**

Templ, M. (2017). *Statistical Disclosure Control for Microdata. Methods and Applications in R*, Springer International Publishing. doi:10.1007/978-3-319-50272-4

Templ, M., Kowarik, A., Meindl, B. (2015). Statistical Disclosure Control for Micro-Data Using the R Package sdcMicro. *Journal of Statistical Software*, 67(4), 1-36. doi:10.18637/jss.v067.i04

*Journal of Statistical Software*, 79(10), 1-38. doi:10.18637/jss.v079.i10

Wednesday 13^{th} 11:10 Case Room 3 (260-055)

## High Dimensional Asymptotics For The Naive Canonical Correlation Coefficient

Mitsuru Tamatani^{1} and Kanta Naito^{2}

^{1}Doshisha University

^{2}Shimane University

**Abstract:** In this talk we investigate the asymptotic behavior of the estimated naive canonical correlation coefficient under the normality assumption and High Dimension Low Sample Size (HDLSS) settings. In general, canonical correlation matrix is associated with canonical correlation analysis which is useful in studying the relationship between two sets of variables. However, in HDLSS settings, the within-class sample covariance matrix \(\hat{\Sigma}\) is singular, because the rank of \(\hat{\Sigma}\) is much less than the number of dimension. To avoid the singularity of \(\hat{\Sigma}\) in HDLSS settings, we utilize the naive canonical correlation matrix with replacing sample covariance matrix by its diagonal part only. We derive the asymptotic normality of the estimated naive canonical correlation coefficient, and compare the results of our numerical studies to the theoretical asymptotic results.

**Keywords:** High dimension low sample size, Naive canonical correlation coefficient, Asymptotic normality

**References:**

Tamatani, M., Koch, I. and Naito, K. (2012). *Journal of Multivariate Analysis*, **111**, 350–367.

Srivastava, M. S. (2011). *Journal of Multivariate Analysis*, **102**, 1190–1103.

*The Annals of Statistics*,

**36**, 2605–2637.

Wednesday 13^{th} 11:10 Case Room 4 (260-009)

## Deep Learning High-Dimensional Covariance Matrices

Philip Yu and Yaohua Tang

Unversity of Hong Kong

**Abstract:** Modeling and forecasting covariance matrices of asset returns play a crucial role in finance. The availability of high frequency intraday data enables the modeling of the realized covariance matrix directly. However, most models in the literature depend on strong structural assumptions and they also suffer from the curse of dimensionality. To solve the problem, we propose a deep learning model which treats each realized covariance matrix as an image. The network structure is designed with simplicity in mind, and yet provides superior accuracy compared with several advanced statistical methods. The model could handle both low-dimensional and high-dimensional realized covariance matrices.

**Keywords:** Deep learning, Realized covariance matrix, Convolutional neural network

**References:**

LeCun, Y., Bottou, L., Bengio, Y. and Haffner, P. (1998). Gradient-based learning applied to document recognition. In *Proceedings of the IEEE*, 86, 2278–2324.

Shen, K., Yao, J. and Li, W. K.(2015). Forecasting High-Dimensional Realized Volatility Matrices Using A Factor Model. *ArXiv e-prints*.

*Journal of the American Statistical Association*, 106, 1025–1040.

Wednesday 13^{th} 11:30 098 Lecture Theatre (260-098)

## R In Industry – Application On Pipe Renewal Planning

Glenn Thomas

Harmonic Analytics

**Abstract:** R has become an increasingly used tool in industry to practically help councils and organisations with their asset management challenges. We will demonstrate some of the practical tools Harmonic Analytics has developed using R to assist in asset management.

One specific example demonstrated will be recent work for a New Zealand council that was experiencing challenges in long term planning around its three waters infrastructure. In particular, challenges stem from the limited information about pipe condition. Using past work order history as proxy for pipe failures, we present a tool that uses a pipe break model to inform replacement strategies. The developed tool allows users to generate and compare both data driven and engineering based scenarios through a variety of lenses, ranging from annual replacement length to service level outcomes. A number of visualisations are available to support comparisons. Data driven scenarios are driven from a variety of perspectives, such as traditional age based replacement, probability of failure and minimising the expected number of pipe breaks across the network.

This kind of work is an exciting step forward, as councils show interest in collaboration and pooling data to improve accuracy.

Wednesday 13^{th} 11:30 OGGB4 (260-073)

## Empirical Comparison Of Some Algorithms For Automatic Univariate ARMA Modeling Using RcmdrPlugin.SPSS

Dedi Rosadi

Universitas Gadjah Mada

**Abstract:** In some application of time series modeling, it is necessary to obtain forecast of various types of data automatically and possibly, in real-time. For instances, to forecast large number of univariate series every day, or to do a real-time processing of the satellite data. Various automatic algorithms for modeling ARMA models are available in the literature, where here we will discuss three methods in particular. One of the method is based on a combination between the best exponential smoothing model to obtain the forecast, together with state-space approach of the underlying model to obtain the prediction interval (see Hyndman, 2007). The second method, which is more advanced method, is based on X-13-ARIMA-SEATS, the seasonal adjustment software by the US Census Bureau (see Sax , 2015). From our previous study in Rosadi (2016), we found that these methods are perform relatively well for SARIMA data. Unfortunately, these approaches do not working well for many of ARMA data. Therefore in paper we extend the study by considering an automatic modeling method based on genetic algorithm approach (see Abo-Hammour, et.al., 2012). These approaches are implemented in our R-GUI package RcmdrPlugin.Econometrics which now already integrated in our new and more comprehensive R-GUI package, namely RcmdrPlugin.SPSS. We provide application of the methods and the tool. From some empirical studies, we found that for ARMA data, the method based on genetic algorithm performs better than the other approaches.

**Keywords:** Automatic ARMA modeling, genetic algorithm, exponential smoothing, X-13-ARIMA, R-GUI

**References:**

Abo-Hammour, Z. E. S., Alsmadi, O. M., Al-Smadi, A. M., Zaqout, M. I., & Saraireh, M. S. (2012). ARMA model order and parameter estimation using genetic algorithms. *Mathematical and Computer Modelling of Dynamical Systems*, **18(2)**, 201–221.

Hyndman, R. J. (2007). forecast: Forecasting functions for time series, R package version 1.05. `URL: http://www.robhyndman.info/Rlibrary/forecast/`

.

Sax, C. (2015). Introduction to seasonal: R interface to X-13ARIMA-SEATS,

`https://cran.r-project.org/web/packages/seasonal/vignettes/seas.pdf`

.

*COMPSTAT 2016*, Oviedo, Spain, 23-26 August 2016.

Wednesday 13^{th} 11:30 OGGB5 (260-051)

## Bayesian Optimum Warranty Length Under Type-II Unified Hybrid Censoring Scheme

Tanmay Sen^{1}, Biswabrata Pradhan^{2}, Yogesh Mani Tripathi^{1}, and Ritwik Bhattacharya^{3}

^{1}Indian Institute of Technology Patna

^{2}Indian Statistical Institute Kolkata

^{3}Centro de Investigacionen Matematicas

**Abstract:** This work considers determination of optimum warranty length under Type-II unified hybrid censoring scheme. Consumers are willing to purchase a highly reliable product with certain cost constraint. To assure the product reliability and also to remain profitable, the manufacturer provides warranties on product lifetime. Moreover, censoredlifetime data are available in practice, to assess the reliability of the product. Therefore, determination of an appropriate warranty length based on censored lifetime data is an important issue to the manufacturer. It is assumed that the lifetime follows a lognormal distribution. We consider a combine free replacement and pro-rata warranty policy (FRW/PRW). The life test is conducted under Type-II unified hybrid censoring scheme. The warranty length is obtained by maximizing an expected utility function.The expectation is taken with respect to the posterior predictive model for time to failure given the available data obtained under Type-II unified hybrid censoring scheme. A real data set is analyzed to illustrate the proposed methodology. We propose a non-linear prorate warranty policy and compare them with linear warranty policy. It is observed that non-linear prorate warranty policy give larger warranty length with maximum profit

**Keywords:**Lognormal distribution, FRW/PRW policies, Optimum warranty length, MH algorithm

Wednesday 13^{th} 11:30 Case Room 2 (260-057)

## Imputation Of The 2016 Economic Census For Business Activity In Japan

Kazumi Wada^{1}, Hiroe Tsubaki^{2}, Yukako Toko^{1}, and Hidemine Sekino^{3}

^{1}National Statistics Center

^{2}Institute of Statistical Mathematics

^{3}The Statistics Bureau

**Abstract:** R has been used in the field of official statistics in Japan for over ten years. This presentation takes up the case of the 2016 Economic Census for Business Activity. The Census aims to identify the structure of establishments and enterprises in all industries on a national and regional level, and to obtain basic information to conduct various statistical surveys by investigating the economic activity of these establishments and enterprises. The major corporate accounting items, such as sales, expenses and salaries, surveyed by the census require imputation to avoid bias. Although ratio imputation is a leading candidate, it is well known that the ratio estimator is very sensitive to outliers; therefore, we need to take appropriate measures for this problem.

Ratio imputation is a special case of regression imputation; however, the conventional ratio estimator has a heteroscedastic error term, which is the obstacle of robustification by means of M-estimation. New robust ratio estimators are developed by segregating the homoscedastic error term with no relation to the auxiliary variable from the original error. The computation of the estimators are made by modifying iterative reweighted least squares (IRLS) algorithm, since it is easy to calculate and fast to converge. The proposed robustified ratio estimator broadens the conventional definition of the ratio estimator with regards to the variance of the error term in addition to effectively alleviating the influence of outliers. The application of the robust estimator is expected to contribute to the accuracy of the Census results.

An random number simulation to confirm the characteristics of these estimators, deciding imputation domains by CART (classification and regression tree), model selection and preparing necessary rates by domain for the census data processing are conducted within the R programming environment.

**Keywords:** GNU R, Outlier, Iteratively reweighted least squares, Ratio estimator, Official statistics

**Acknowledgement:**This work was supported by JSPS KAKENHI Grant Number JP16H02013.

Wednesday 13^{th} 11:30 Case Room 4 (260-009)

## Applying Active Learning Procedure To Drug Consumption Data

Yuan-Chin Chang

Academia Sinica

**Abstract:** We apply the method of active learning to build a binary classification model for drug consumption data. Due to the nature of active learning, subject selection is an major issue is its learning process. There are many kinds of subject selection schemes proposed in the literature. The subject recruiting procedure may also depend on its learning target criterion such as accuracy, area under ROC curve and so on. Moreover, in practical active learning scenarios, the label information of samples can only be revealed as they are recruited into training data set, and we will pay the domain experts to label these selected sample. Therefore, to consider the labelling cost, how/when to stop an active learning procedure is always an important and challenging problem in active learning. In this talk, we propose an active learning procedure targeting at area under an ROC curve, and based on the idea of robustness, we then used a modified influential index to locate the most informative samples, sequentially, such that the learning procedure can achieve the target efficiently. We then apply our procedure to drug consumption data sets.

**Keywords:** ROC curve, area under curve, active learning, influential index

**References:**

Calders, T. and Jaroszewicz, S. (2007). Efficient auc optimization for classification. In *Knowledge Discovery in Databases: PKDD 2007*, pages 42–53. Springer.

Wednesday 13^{th} 11:50 098 Lecture Theatre (260-098)

## R For Everything

Jared Lander

Lander Analytics

**Abstract:** Everyone knows I love R. So much that I never want to leave the friendly environs of R and RStudio. Want to download a file? Use `download.file`

. Want to create a directory? Use `dir.create`

. Sending an email? `gmailr`

. Using Git? `git2r`

. Building this slideshow? `rmarkdown`

. Writing a book? `knitr`

. Let’s take a look at everyday activities that can be done in R.

**Keywords:** R, RMarkdown, knitr, email, football, git, download, data, plotting, modeling, logistic regression

**References:**

*R for Everyone, Second Edition.*New York: Addison-Wesley.

Wednesday 13^{th} 11:50 OGGB4 (260-073)

## R Package For New Two-Stage Methods In Forecasting Time Series With Multiple Seasonality

Anupama Lakshmanan and Shubhabrata Das

Indian Institute of Management Bangalore

**Abstract:** Complex multiple seasonality is an important emerging challenge in time series forecasting. We propose a framework that segregates the task into two stages. In the first stage, the time series is aggregated at the low frequency level (such as daily or weekly) and suitable methods such as regression, ARIMA or TBATS, are used to fit this lower frequency data. In the second stage, additive or multiplicative seasonality at the higher frequency levels may be estimated using classical, or function-based methods. Finally, the estimates from the two stages are combined.

In this work, we build a package for implementing the above two-stage framework for modeling time series with multiple levels of seasonality within R. This would make it convenient to execute and possibly lead to more practitioners and academicians adopting it. The package would allow the user to decide the specific methods to be used in the two stages and also the separation between high and low frequency. Errors are calculated for both model and validation period, which may be selected by the user and model selection choices based on different criterion will be facilitated. Forecast combination may also be integrated with the developed routine. The schematics will be presented along with demonstration of the package in several real data sets.

**Keywords:**Additive seasonality, ARIMA, forecast combination, high frequency, low frequency, multiplicative seasonality, polynomial seasonality, regression, TBATS, trigonometric seasonality

Wednesday 13^{th} 11:50 Case Room 2 (260-057)

## Analysis Of Official Microdata Using Secure Statistical Computation System

Kiyomi Shirakawa^{1,3}, Koji Chida^{2}, Satoshi Takahashi^{2}, Satoshi Tanaka^{2}, Ryo Kikuchi^{2}, and Dai Ikarashi^{2}

^{1}National Statistics Center

^{2}NTT

^{3}Hitotsubashi University

**Abstract:** We introduce some important functions on a secure computation system and empirically evaluate them using the statistical computing software R. The secure computation is a cryptographic technology that enables us to operate data while keeping the data encrypted. Due to the remarkable aspect, we can construct a secure on-line analytical system to protect against unauthorized access, computer virus and internal fraud. Moreover, the function of secure computation has a benefit for privacy.

So far, we developed a secure computation system that runs R as a front-end application. In this research, we focus on the analysis of official microdata using our secure computation system. By employing the R script language to secure computation, we can potentially make new functions for the analysis of official microdata on our secure computation system. We show some examples of functions on the system using the R script language. A demonstration experiment to verify the practicality and scalability of the system in the field of official statistics is also in our scope.

**Keywords:**Secure Computation, Security, Privacy, Big Data, Official Statistics, R

Wednesday 13^{th} 11:50 Case Room 4 (260-009)

## Presenting Flexi, A Statistical Program For Fitting Variance Models

Martin Upsdell

AgResearch

**Abstract:**Flexi is a statistical program designed to fit variance based models. In this talk I will explore the advantages and disadvantages of the variance based model compared to the more commonly adopted mean based approach. Several examples will be given where the properties of variance based models provide a clearer understanding of the data. To illustrate the differences in the approach to the data I will compare Television and Progressive Graphics File methods of transferring a picture. The Television builds up the global picture from individual pixels describing a local area of the picture, whereas the Progressive Graphics File proceeds from the global value of the median colour of the whole picture to the local value of each individual pixel by successive refinements. This gives a coarse blocky picture at the start which refines into a detailed picture at the end. Mean based models are like television pictures whereas variance based models are like Progressive Graphics File pictures. The advantages and disadvantages of the two methods will be discussed.

Keynote: Wednesday 13^{th} 13:20 098 Lecture Theatre (260-098)

## Space And Circular Time Log Gaussian Cox Processes With Application To Crime Event Data

Alan Gelfand

Duke University

**Abstract:** We view the locations and times of a collection of crime events as a space-time point pattern modeled as either a nonhomogeneous Poisson process or a more general log Gaussian Cox process. We need to specify a space-time intensity. Viewing time as circular, necessitates a valid separable and nonseparable covariance functions over a bounded spatial region crossed with circular time. Additionally, crimes are classified by crime type and each crime event is marked by day of the year which we convert to day of the week.

Wednesday 13^{th} 14:10 098 Lecture Theatre (260-098)

## Cluster-Wise Regression Models Combined By A Quasi-Linear Function

Kenichi Hayashi^{1}, Katsuhiro Omae^{2}, and Shinto Eguchi^{3}

^{1}Keio University

^{2}The Graduate University for Advanced Studies

^{3}Institute of Statistical Mathematics

**Abstract:** Suppose that there are multiple heterogeneous subgroups in a dataset. In the “Big data” era, this would be a natural assumption for many fields of application such as medicine, biology, marketing, psychology, etc. Then, conventional linear regression models result in not only poor prediction performance but also misleading interpretation of analyses. In this study, we propose an extension of cluster-wise regression models \(\phi^{-1}\left(\sum_{k=1}^Kp_k(\vec{x})\phi(\vec{\beta}_k^\top\vec{x})\right)\), where \(\phi\) is a strictly increasing function, \(\vec{x}\in\mathbb{R}^d\), \(\vec{\beta}_k\) is a regression coefficient for \(k\)th cluster and \(p_k(\vec{x})\) is a non-negative function satisfying \(\sum_{k=1}^Kp_k(\vec{x})=1\) for any \(\vec{x}\). We show that the proposed model has flexibility in clustering and “averaging” multiple regressors and hence includes the existing methods such as Späth (1981), DeSarbo et al. (1989) as special cases.

**Keywords:** Cluster-wise regression, Generalized linear models, Population heterogeneity

**References:**

DeSarbo, W.S., Oliver, R.L., and Rangaswamy, A. (1989). A simulated annealing methodology for clusterwise linear regression. *Psychometrika*, **54**, 707–736.

*Computing*,

**22**, 367–373.

Wednesday 13^{th} 14:10 Case Room 1 (260-005)

## Hierarchical Structural Component Analysis Of Gene-Environment Interactions

Sungkyoung Choi^{1}, Seungyeoun Lee^{2}, and Taesung Park^{3}

^{1}Yonsei University

^{2}Sejong University

^{3}Seoul National University

**Abstract:** Gene-environment interactions (GEI) are known to be one possible avenue for addressing the missing heritability problem in genome-wide association studies (GWAS). Although many statistical methods have been proposed for identifying and analyzing GEI, most of these consider interactions between a single genetic variants such as single nucleotide polymorphism (SNPs) by the environment. In this study, we proposed a new statistical method for gene-based GEI analysis, Hierarchical structural CoMponent analysis of Gene-Environment Interaction (HisCoM-GEI). HisCoM-GEI is based on generalized structured component analysis, and can consider hierarchical structural relationships among SNPs in a gene. HisCoM-GEI can effectively aggregate all possible pairwise SNP-Environment interactions into a latent variable by imposing a ridge penalty, from which it then performs GEI analysis. Furthermore, HisCoM-GEI can evaluate both gene-level and SNP-level analyses. We applied the HisCoM-GEI to the cohort data of the Korea Associated Resource (KARE) consortium to identify GEIs between genes and alcohol intake on the blood pressure traits.

**Keywords:**Gene-environment interaction, SNP, gene, GWAS

Wednesday 13^{th} 14:10 OGGB5 (260-051)

## Wavelet-Based Power Transformation Of Non-Gaussian Long Memory Time Series

Kyungduk Ko^{1} and Chul Eung Kim^{2}

^{1}Boise State University

^{2}Yonsei University

**Abstract:** We consider a power transformation through the well-known Box-cox transformation to induce normality from non-Gaussian long memory processes and propose a Bayesian method to simultaneously estimate the transformation parameter and long memory parameter. To ease computational burdens due to the dense variance-covariance matrix of long memory time series, we base our statistical inference on the wavelet domain rather than the original data domain. For a joint estimation of the parameters of interest, posterior estimations are carried out via Markov chain Monte Carlo (MCMC). An application to German stock return data is presented.

**Keywords:** Box-Cox transformation, Discrete wavelet transform, Long memory, MCMC, Normality

**References:**

Dahlhaus, R. (1990). Efficient location and regression estimation for long range dependent regression models. *Annuals of Statistics*, 23, 1029–1047.

Ko, K. and Lee, J. (2008). Confidence intervals for long memory regressions. *Statistics and Probability Letters*, 78, 1894–1902.

*Applied Stochastic Models in Business and Industry*,

**23**, 493–502.

Wednesday 13^{th} 14:10 Case Room 2 (260-057)

## Cross Covariance Estimation For Integration Of Multi-Omics Data

Johan Lim^{1}, Hiromi Koh^{2}, and Hyungwon Choi^{2}

^{1}Seoul National University

^{2}National University of Singapore

**Abstract:** In integrative analysis of multiple types of -omics data, it is often of interest to infer associations between two different types of molecules. The prevailing analysis methods depend on ensemble of brute-force pairwise univariate association tests between the two types, best exemplified by expression quantitative loci (eQTL) mapping. In a nutshell, this problem can be generally framed as a sparse cross-covariance matrix. In this work, we propose a two-stage estimator of cross covariance matrix \({\mathbf{\Sigma_{XY}}}\) between \(p\)-vector \({\mathbf{X}}\) and \(q\)-vector \({\mathbf{Y}}\), assuming that the two variables have regulatory relationships and that we know a group structure in the variables in \({\mathbf{X}}\). We first decompose the covariance matrix of \({\mathbf{X}}\), \({\mathbf{\Sigma_{XX}}}\), into systematic covariance consistent with the functional group information \({\mathbf{\Sigma_{XX}}}^{(G)}\) and the residual covariance not explained by the group information \({\mathbf{\Sigma_{XX}}}^{(R)}\). Following this decomposition, we estimate the cross covariance matrix by multi-response group lasso, yielding \({\mathbf{\Sigma_{XY}}}= {\mathbf{\Sigma_{XX}}}{\mathbf{B}}_{(p \times q)} = ({\mathbf{\Sigma_{XX}}}^{(G)} + {\mathbf{\Sigma_{XX}}}^{(R)}) {\mathbf{B}}_{(p \times q)}\). As a result of this decomposition, \({\mathbf{\Sigma_{XY}}}\) can also be expressed as the sum of a systematic term and a residual term, breaking down the cross-covariance into a fraction attributable to pathway-level regulation and the rest. We applied the method to epigenetic regulation analysis of mRNA expression by DNA methylation in the The Cancer Genome Atlas invasive breast cancer cohort.

**Keywords:** Cross covariance matrix, data integration.

**References:**

Simon, N., Friedman, J. and Hastie, T. (2013). *A Blockwise Descent Algorithm for Group-penalized Multiresponse and Multinomial Regression*

*Nature*,

**490**, 61-70.

Wednesday 13^{th} 14:10 Case Room 3 (260-055)

## Relationships Between Linguistic Characteristics And The Use Of Māori Loanwords In New Zealand English.

Steven Miller and Andreea Calude

University of Waikato

**Abstract:** We present the initial results from a project looking at the linguistic and socio-linguistic characteristics that affect the prevalence of Māori loanwords in the use of New Zealand English, and describe the paths we see this research taking in the next few years.

Loanwords are words that originate in one language (the donor language) and enter into, and are productively used within another language (the host language). For our initial research, we were particularly interested in the use of Māori loanwords in spoken New Zealand English, as found within the Wellington Corpus of Spoken New Zealand English.

We used generalised linear mixed effects models to determine if there were significant relationships between the linguistic characteristics of the loanwords used / words replaced, demographic features of the speakers, and the ethnicity of the audiences.

We found that linguistic characteristics of the loanwords and their English counterparts affect the probability of using the loanword for both Pākehā and Māori speakers, there was a difference in the probability of using a loanword between the sexes for Māori speakers only, and Māori speakers moderated the use of loanwords in conversations depending on the ethnicity of their audience.

We will briefly describe the next phase of the research that will use network modelling to characterise the use of Māori loanwords in written media.

**Keywords:**Linguistics, loanwords, Māori, GLMM

Wednesday 13^{th} 14:10 Case Room 4 (260-009)

## Transfer Regression And Predictive Distributions

Shigetoshi Hosaka^{1} and Jinfang Wang^{2}

^{1}Hosaka Clinic of Internal Medicine

^{2}Chiba University

**Abstract:** We introduce the *transfer regression*, a method for constructing prior distributions for parameters defining generalized linear models (GLM). The transfer regressions are based frequency tables, usually obtained by categorizing the continuous variables. So obtained prior information are transferred to the parameters defining the second stage GLM based on detailed data. at the second stage based on more detailed data. We illustrate these ideas by showing how to compute posterior predictive probabilities of contracting diabetes based on HbA1c data obtained from comprehensive medical examinations.

**Keywords:** Bayesian generalized linear models, Markov chain Monte Carlo methods, posterior predictive distributions

**References:**

Andrew D. Martin, Kevin M. Quinn and Jong Hee Park (2011). MCMCpack: Markov Chain Monte Carlo in R, *Journal of Statistical Software*, **42**, 1–21.

Kass, R. E. and Wasserman, L. (1996). The Selection of Prior Distributions by Formal Rules, *Journal of the American Statistical Association*, **91**, 1343–1370.

*Statistical Modelling and Computational Algorithms*”, at Nagoya University, Febuary 18–19, 2017.

Wednesday 13^{th} 14:30 098 Lecture Theatre (260-098)

## An Overview Of The Correspondence Analysis Family

Eric Beh

University of Newcastle

**Abstract:** Correspondence analysis (CA) is well known to be a member of the family of multivariate analysis techniques and is concerned with the visualisation of the association between two or more categorical variables. The classic texts of Greenacre (1984) and Lebart, Morineau and Warwick (1984), for example, provide an excellent technical, practical and historical account of development of CA up to that period. What is less well known is that the literature on CA extends well beyond the traditional approaches that can be found in many multivariate texts and often there are disciplines that redefine the way in which it is performed. For example, the various fields of ecology have successfully germinated variants including *canonical correspondence analysis* and *detrended correspondence analysis*. However the scope, and literature, of CA is not confined to these examples. Beh and Lombardo (2014, Section 1.6.3) and provide a comprehensive list of members of the “family” which, now, number about 50 members. I shall provide an overview of some of the popular, and not-so-popular, members of the CA family.

**Keywords:** Correspondence analysis, Multiple CA, Family of analyses

**References:**

Beh, E. J. and Lombardo, R. (2014). *Correspondence Analysis: Theory, Practice and New Strategies*. Chichester: Wiley.

Greenacre, M. J. (1984), *Theory and Applications of Correspondence Analysis*. London: Academic Press.

*Multivariate Descriptive Statistical Analysis*. New York: John Wiley & Sons.

Wednesday 13^{th} 14:30 Case Room 1 (260-005)

## Testing For Genetic Associations In Arbitrarily Structured Populations

Minsun Song

Sookmyung Women’s University

**Abstract:** We present a new statistical test of association between a trait and genetic markers, which we theoretically and practically prove to be robust to arbitrarily complex population structure. The statistical test involves a set of parameters that can be directly estimated from large-scale genotyping data, such as those measured in genome-wide associations studies. We also derive a new set of methodologies, called a genotype-conditional association test, shown to provide accurate association tests in populations with complex structures, manifested in both the genetic and non-genetic contributions to the trait. We demonstrate the proposed method on a large simulation study and on the real data. Our proposed framework provides a substantially different approach to the problem from existing methods.

**Keyword:**Genome-wide association studies, Latent variable, Population structure

Wednesday 13^{th} 14:30 OGGB5 (260-051)

## Threshold Determination For The Meteorological Data Quality Control In Korea

Yung-Seop Lee^{1}, Hee-Kyung Kim^{1}, and Myungjin Hyun^{2}

^{1}Dongguk University

^{2}KMA National Climate Data Center

**Abstract:** The raw meteorological data need to be cleaned since they are from the diverse sources such as ASOS(Automated Synoptic Observing System) and AWS(Automatic Weather Station). The meteorological data in South Korea is observed from about 100 ASOS and 500 AWS. In order to produce the high qualified meteorological data, several data quality control algorithms are applied. In this study, cluster analysis for almost 600 meteorological sites is applied depending on their climatic characteristics. After clustering, we propose the several threshold algorithms in the given cluster. The proposed threshold values for data quality control algorithms will be adequate to Korea climate condition by cluster and month. Thresholds of QC algorithms, which are step test, persistence test and climate range test, are determined. Through these algorithms and threshold, the qualified meteorological data can be produced for the improved forecast accuracy.

**Keywords:**meteorological data quality control, threshold values, cluster analysis, step test, persistence test, climate range test.

Wednesday 13^{th} 14:30 Case Room 2 (260-057)

## Regularized Noise-Reduction Methodology For High-Dimensional Data

Kazuyoshi Yata and Makoto Aoshima

University of Tsukuba

**Abstract:** In this talk, we consider principal component analysis (PCA) methods in high-dimensional settings. We first consider asymptotic properties of the conventional estimator of eigenvalues. We show that the estimator is affected by the high-dimensional noise structure directly, so that it becomes inconsistent. In order to overcome such difficulties in a high-dimensional situation, Yata and Aoshima (2012) developed a new PCA method called the noise-reduction (NR) methodology. We show that the NR method can enjoy consistency properties not only for eigenvalues but also for PC directions in high-dimensional settings. The estimator of the PC directions by the NR method has a consistency property in terms of an inner product. However, it does not hold a consistency property in terms of the Euclid norm. With the help of a thresholding method, we modify the estimator and propose a regularized NR method. We show that it holds the consistency property of the Euclid norm. Finally, we check the performance of the new NR method by using microarray data sets.

**Keywords:** eigenstructure, large \(p\) small \(n\), PCA, spiked model

**References:**

*Journal of Multivariate Analysis*,

**105**, 193–215.

Wednesday 13^{th} 14:30 Case Room 3 (260-055)

## Computation Of Influence Functions For Robust Statistics

Maheswaran Rohan

Auckland University of Technology

**Abstract:** Robust statistics are often computed when outliers are present. One of the diagnostics tools for assessing the robustness of estimation is the influence function, which measures the impact on a statistic of adding new data to or removing existing data from the data set. It is also useful for computing the standard error of the statistic.

The computation of influence function for closed form estimates is relatively easy in comparison to that for non-closed form estimates. However, robust statistics are often not in closed form and are computed using iterative algorithms. Obtaining the analytical form of the empirical influence functions of robust statistics for multiple parameters is rare in the current literature and not easy.

In this talk, I use matrix algebra including matrix derivation to show how influence functions for robust statistics can be obtained analytically, particularly in M-estimators with multiple of parameter vectors.

**Keywords:**Keywords M-estimators, One-step influence function, Jacobian matrix

Wednesday 13^{th} 14:30 Case Room 4 (260-009)

## Adaptive Model Averaging In High-Dimensional Linear Regression

Tzu-Chang Forrest Cheng^{1}, Wei-Cheng Hsiao^{2}, and Ching-Kang Ing^{2}

^{1}National Central University

^{2}National Tsing Hua University

**Abstract:** This paper aims to propose a data-adaptive model averaging estimation in the high-dimensional framework. To this end, We first consider the orthogonal greedy algorithm (OGA) proposed by Ing and Lai (2011) to construct a set of nested models. The high-dimensional model averaging criteria (HDMMA) suggested by Ing (2016) is considered upon the OGA nested models, while the penalty term is unknown and needed to be estimated. We then use the cross-validation to select the optimal penalty. This method of penalty selection is shown to be optimally adaptive to a wide class of data generating processes. Furthermore, the resultant HDMMA estimator based on the selected penalty is shown to be asymptotic rate efficient. Finally, numerical studies in this paper are expected to shed some light on the choice of data splitting ratio for the cross-validation.

**Keywords:** Adaptive penalty, Cross-validation, High dimension, Model averaging, Greedy algorithm

**References:**

Ing, C.-K. and Lai, T. L. (2011). A stepwise regression method and consistent model selection for high-dimensional sparse linear models. *Statist. Sinica*, **21**, 1473–1513.

*Unpublished Technical Report*.

Wednesday 13^{th} 14:50 098 Lecture Theatre (260-098)

## Model-Based Clustering For Multivariate Categorical Data With Dimension Reduction

Michio Yamamoto

Okayama University

**Abstract:** A novel model-based clustering procedure for multivariate categorical data is proposed. The proposed model assumes that each response probability has a low-dimensional representation of the cluster structure, which is constructed by weights for categorical variables and scores for cluster representatives. For the visualization of the cluster structure, we define low-dimensional scores for individuals as convex combinations of scores for cluster representatives, which may be interpretable in a similar manner to the archetypal analysis developed by Cutler and Breiman (1994). Because the proposed model has the so-called rotational indeterminacy, it is needed to conduct rotation methods after parameter estimation to obtain interpretable results. Instead of this two-step approach, we develop a penalized likelihood procedure that imposes a sparsity-inducing penalty on the weights for categorical variables. To optimize the proposed penalized likelihood criterion, we develop an expectation-maximization (EM) algorithm with gradient projection and coordinate descent. It is shown that there is trade-off relation between the convergence rate of the algorithm and the cluster recovery.

**Keywords:** clustering, categorical data, dimension reduction, EM algorithm, sparse estimation

**References:**

Cutler, A., Breiman, L. (1994). Archetypal analysis. *Technometrics*, **36**, 338–347.

*Pattern Recognition*,

**48**, 3959–3968.

Wednesday 13^{th} 14:50 Case Room 1 (260-005)

## Phylogenetic Tree-Based Microbiome Association Test

Sungho Won

Seoul National University

**Abstract:** Microbial metagenomics data has large inter-subject variation and operational taxonomic units (OTU) for each species are usually very sparse. Because of these problems, non-parametric approaches such as Mann-Whitney U test and Wilcoxon rank-sum test have been utilized. However these approaches suffer from low statistical powers for association analyses and thus investigation on efficient statistical analyses is necessary. Main goal in my thesis is to propose phylogenetic Tree-based Microbiome Association Test (TMAT) for association analyses between microbiome abundances of each OTU and disease phenotype. Phylogenetic tree reveals similarity between different OTUs, and thus was used to provide TMAT. TMAT calculates score test statistics for each node and test statistics for all nodes are combined into a single statistics by minimum p-value or Fisher’s combing p-value method. TMAT was compared with existing methods with extensive simulations. Simulation studies show that TMAT preserves the nominal type-1 error and its statistical powers were usually much better than existing methods for considered scenarios. Furthermore it was applied to atopic diseases and found that community profiles of Enterococcus is associated.

**Keywords:**NGS; phylogenetic treel Microbiome Association Test

Wednesday 13^{th} 14:50 OGGB5 (260-051)

## Fitting Additive Hazards Model Using Calibrated Weights For Case-Cohort Data

Hyuntae Kyung and Sangwook Kang

Yonsei University

**Abstract:** A case-cohort design is an efficient study design for analyzing failure time data by reducing the cost and effort of conducting a large cohort study. Estimation of regression coefficients is typically done through a weighted estimating equation approach whose weight is the inverse of the sampling probabilities. Several techniques to enhance the efficiency by estimating weights or calibrating weights based on auxiliary variables have been developed for Cox models. In this paper, we propose to extend these methodologies to semiparametric additive hazards models. The proposed estimators are demonstrated to be more efficient, via simulation studies, than the usual Horvitz-Thompson type estimator. We illustrate a use of the proposed estimators by using the National Wilms Tumor Study data.

**Keywords:**Estimating Equations, Semiparametric Model, Survey Sampling, Survival Analysis

Wednesday 13^{th} 14:50 Case Room 2 (260-057)

## Selecting The Number Of Principal Components

Yunjin Choi

National University of Singapore

**Abstract:** Principal Component Analysis (PCA) is one of the most popular methods in multivariate data analysis, which can be applied to covariance matrices. Despite the popularity of the method, there is no widely adopted standard approach to select the number of principal components to retain. To address this issue, we propose a novel method utilizing the hypothesis testing framework and test whether the currently selected principal components capture all the statistically significant signals in the given data set. While existing hypothesis testing approaches do not enjoy the exact type 1 error property and lose power under some scenarios, the proposed method provides an exact type 1 error control along with decent size of power in detecting signals. Central to our work is the post-selection inference framework which facilitates valid inference after data-driven model selection; the proposed hypothesis testing method provides exact type 1 error controls by conditioning on the selection event which leads to the inference. We also introduce a possible extension of the proposed method for high-dimensional data.

**Keywords:**Principal component analysis, post-selection inference, hypothesis testing

Wednesday 13^{th} 14:50 Case Room 3 (260-055)

## Rolling Survival Extrapolation Algorithm For Estimating Life Years Lost Among Subjects Exposed To Long-Term Air Pollution

Jing-Shiang Hwang and Tsuey-Hwa Hu

Academia Sinica

**Abstract:** Measure of expected years of life lost (EYLL) of a cohort of subjects living with specific conditions would be useful for quantifying and thereby comparing the societal burden of different conditions. One promising approach of estimating EYLL is based on relative survival between the index cohort and an age- and sex-matched reference population generated from vital statistics to extrapolate survival function of the index cohort. The EYLL is then estimated by computing the area between the survival curve of the reference population and extrapolated survival curve of the index cohort. In this talk, we will introduce our newly developed method called rolling survival extrapolation algorithm which consists of two major stages. First, we apply logit transformation to the relative survival so that the transformed curve beyond follow-up would approximate to a nearly straight line. Second, similar to the rolling forecast process for predicting the future over a set period of time, we take advantage of the accurate short-term extrapolation of restricted cubic splines models to guide the transformed relative survival forward step-by-step using the model updated data. There are some studies that provide general evidence for long-term associations of air pollution with hospital admissions and death of various causes. We have found no published epidemiological studies on the effects of long-term air pollution exposure and life years lost. With the proposed method, we estimate EYLL from long-term exposure to air pollution among Taiwanese adult population at rural township and city district levels. The results show that elderly people living in a worse local air pollution for decades long had more expected years of life lost after adjusting social economic status.

**Keywords:**Life expectancy, expected years of life lost, air pollution health effects, particulate matter

Wednesday 13^{th} 14:50 Case Room 4 (260-009)

## Enhancing The Flexibility Of Regression Modeling By Liquid Association

Ker-Chau Li

Academia Sinica

**Abstract:** Multivariate regression aims at the study of the relationship between one set of input variables X and one set of output variables Y. Challenges occur when no parametric model is known and yet the number of variables is large. To overcome the difficulties, dimension reduction methods under the inverse regression viewpoint have been investigated by many authors. Liquid association (LA) depicts the change in the covariation of two variables X and Y as a third variable Z varies. In this talk, I will describe a framework to illustrate how the LA methodology can help increase the modeling flexibility of multivariate regression in analyzing complex data.

**Keywords:**Sliced inverse regression, liquid association

Wednesday 13^{th} 15:10 098 Lecture Theatre (260-098)

## Clusterwise Low-Rank Correlation Analysis Based On Majorization

Kensuke Tanioka^{1}, Satoru Hiwa^{2}, Tomoyuki Hiroyasu^{2}, and Hiroshi Yadohisa^{2}

^{1}Wakayama Medical University

^{2}Doshisha University

**Abstract:** Given correlation matrices between variables of subjects and these classes of subjects, it is important to get the distinctive local networks for each class. For example, in fMRI data analysis, such the situation is observed. In concretely, each correlation matrix between regions of interests for his/her brain is observed, and each information of class is get through the experiment. In this presentation, to achieve the purpose, we proposed simultaneous analysis for both clustering of variables and low-rank approximation of correlation matrices corresponding to each class. For the estimation, we adopt the majorization algorithm based on Pietersz and Groenen (2004) and Simon and Abell (2010). Through the proposed method, we can get the distinctive sparse correlation matrices corresponding to classes, while we have to determine the number of clusters.

**Keywords:** sparse estimation, clustering variables, ALS

**References:**

Pietersz, R., and Groenen, J.F (2004). *Rank Reduction of Correlation Matrices by Majorization.* Quant.Finance, **4**: 649–662.

*Majorization Algorithm for Constrained Correlation Matrix Approximation*, Linear Algebra and its Apprications,,

**432**, 1152-1164.

Wednesday 13^{th} 15:10 OGGB5 (260-051)

## Bayesian Analysis For Fitting Zero-Inflated Count Data With Data Augmentation

Beomseuk Hwang^{1} and Zhen Chen^{2}

^{1}Chung-Ang University

^{2}National Institutes of Health

**Abstract:** Count data with excess zeros are common in epidemiological studies. Zero-inflated Poisson (ZIP) model or zero-inflated negative binomial (ZINB) model can be usually used in these cases. From Bayesian perspective, however, the ZIP and ZINB models are not straightforward to fit, usually requiring manual tunings in the Markov chain Monte Carlo algorithm. We consider the auxiliary mixture sampling through several data augmentations that effectively transform the non-linear and non-Gaussian problem in zero-inflated regression model into a set of linear and Gaussian one. The auxiliary mixture sampling results in tuning-free algorithms in MCMC. We demonstrate how the auxiliary mixture sampling can be applied to an epidemiological case study.

**Keywords:**Auxiliary mixture sampling, ZIP model, ZINB model, Markov chain Monte Carlo

Wednesday 13^{th} 15:10 Case Room 2 (260-057)

## Towards A Sparse, Scalable, And Stably Positive Definite (Inverse) Covariance Estimator

Joong-Ho Won

Seoul National University

**Abstract**: High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. The problem is notoriously difficult in high dimensions as the traditional estimate is not even positive definite. An important line of research in this regard is to shrink the extreme spectrum of the covariance matrix estimators. A separate line of research in the literature has considered sparse inverse covariance estimation which in turn gives rise to graphical models. In practice, however, a sparse covariance or inverse covariance matrix which is simultaneously well-conditioned and at the same time computationally tractable is desired. There has been little research at the confluence of these three topics. In this paper we consider imposing a condition number constraint to various types of losses used in covariance and inverse covariance matrix estimation. This extends the approach by Won, Lim, Kim, and Rajaratnam (2013) on multivariate Gaussian log likelihood. When the loss function can be decomposed as a sum of an orthogonally invariant function of the estimate and its inner product with a function of the sample covariance matrix, we show that a solution path algorithm can be derived, involving a series of ordinary differential equations. The path algorithm is at- tractive because it provides the entire family of estimates for all possible values of the condition number bound, at the same computational cost of a single estimate with a fixed upper bound. An important finding is that the proximal operator for the condition number constraint, which turns out to be very useful in regularizing loss functions that are not orthogonally invariant and may yield non-positive-definite estimates, can be efficiently computed by this path algorithm. As a concrete illustration of its practical importance, we develop an operator-splitting algorithm that imposes a guarantee of well-conditioning as well as positive definiteness to recently proposed convex pseudo-likelihood based graphical model selection methods (Zhang and Zou, 2014; Khare, Oh, and Rajaratnam, 2015).

Wednesday 13^{th} 15:10 Case Room 3 (260-055)

## Tick-By-Tick Effect On The Inference Of Ultra-High Frequency Data

Zhi Liu

University of Macau

**Abstract:**In the inference of ultra-high frequency data, the existing methods are challenged by the tick-by-tick effect, namely, the transactions recorded simultaneously at a time point. In this talk, we will discuss how it influences the estimation of integrated volatility matrix. The effect of microstructure noise and jumps will be discussed as well. We propose to use a double-averaging procedure to deal with these issues. The related asymptotic distribution of the proposed estimator is established. Even interestingly, the double-averaging estimator achieves the “oracle”" property, that is, the asymptotic efficiency is the same as that of the case that the exact trading time of transactions are fully observed. Simulation studies support the theoretical results. The estimation procedure is illustrated through a real data analysis.

Wednesday 13^{th} 15:10 Case Room 4 (260-009)

## High Mortality Predictions With Lines Or Curves Fitted To Over-Dispersed Exposure-Mortality Data

John Maindonald

Statistics Research Associates

**Abstract:**Two types of models are considered and compared. The first is a generalized linear model with logit link, with quasibinomial error, and with weighting function that is designed to give reduced weights at the two ends of the scale, relative to mortalities of around 50%. The other approach is to apply a logit transform, and then use a linear model. The logit transformed data appears, for the data that motivated this paper, consistent with the usual linear model variance homogeneity assumptions. For use of a generalized linear model, the standard linear model diagnostics require modifica- tion so that high mortality points do not unduly distort the smooth that is standardly shown for the scale-location plot. A further issue is that 100% mortality points appear to distort a response that, for mortalities less than 100%, is close to linear on the scale of the link function.

Wednesday 13^{th} 16:00 098 Lecture Theatre (260-098)

## Lattice Polytope Samplers

Martin Hazelton

Massey University

**Abstract:** Statistical inverse problems occur when we wish to learn about some random process that is observed only indirectly. Inference in such situations typically involves sampling possible values for the latent variables of interest conditional on the indirect observations. This talk is concerned with inverse problems for count data, for which the latent variables are constrained to lie on the integer lattice within a convex polytope (a bounded multidimensional polyhedron). An illustrative example arises in transport engineering where we observe vehicle counts entering or leaving each zone of the network, then want to sample possible interzonal patterns of traffic flow consistent with those entry/exit counts. Other problems with this structure arise when conducting exact inference for contingency tables, and when analysing capture-recapture data in ecology.

In principle such sampling can be conducted using Markov chain Monte Carlo methods through a random walk on the lattice polytope, but it is challenging to design algorithms for doing so that are both computationally efficient and have guaranteed theoretical properties. The seminal work of Diaconis and Sturmfels (1998) on Markov bases addresses some of the theoretical issues, but has significant practical limitations. In this talk I shall discuss some preliminary findings based on a more geometric approach to sampler design.

**Keywords:** lattice bases, Markov bases, MCMC, statistical linear inverse problem

**References:**

*The Annals of Statistics*

**26**, 363-397.

Wednesday 13^{th} 16:00 Case Room 4 (260-009)

## Statistical Modelling And Analysis Of Cosmic Microwave Background Data

Andriy Olenko

La Trobe University

**Abstract:** Analysis of the Cosmic Microwave Background (CMB) radiation is a remarkable research area in cosmology whose results won two Nobel prizes in physics in 1978 and 2006 for the discovery of the CMB radiation and its anisotropy. Spurred on by a wealth of satellite data, intensive investigations in the past few years have resulted in many relevant physical and mathematical formalisms to describe and characterise CMB radiation. At the same time, these investigations have raised a number of challenges, theoretical and practical. Studies of deviations from isotropy and Gaussianity, the two fundamental assumptions of cosmological models of the early Universe, form the core of recent experimental and theoretical research in cosmology.

Recent results on modelling CMB evolution and approximation of corresponding random fields will be discussed. Some new approaches to test Gaussianity using multifractality will be illustrated using CMB data. Finally, a new R package for CMB data will be presented.

The presentation is based on joint research with Vo Anh (QUT), N.Leonenko (Cardiff university), P.Broadbridge, D. Fryer, Yu.G. Wang (La Trobe University). This research was supported under the Australian Research Council’s Discovery Project DP160101366.

**Keywords:** random fields, spatial statistics, cosmic microwave background data, R package

**References:**

Wednesday 13^{th} 16:00 OGGB5 (260-051)

## Measure Of Departure From Marginal Average Point-Symmetry For Two-Way Contingency Tables With Ordered Categories

Kiyotaka Iki

Tokyo University of Science

**Abstract:** For the analysis of two-way contingency tables with ordered categories, Yamamoto, Tahata, Suzuki and Tomizawa (2011) considered a measure to represent the degree of departure from marginal point-symmetry. The maximum value of the measure cannot distinguish two kinds of marginal complete asymmetry with respect to the midpoint. The present article proposes a measure which can distinguish two kinds of marginal asymmetry with respect to the midpoint. It also gives large-sample confidence interval for the proposed measure.

**Keywords:** Asymmetry, marginal proportional point-symmetry, marginal point-symmetry, measure, model, ordered category

**References:**

Tomizawa, S. (1985). *Biometrical Journal*, **27**, 895–905.

Wall, K.D. and Lienert, G.A. (1976). *Biometrical Journal*, **18**, 259–264.

*Statistica*,

**71**, 367–380.

Wednesday 13^{th} 16:00 Case Room 2 (260-057)

## Sparse Estimates From Dense Precision Matrix Posteriors

Beatrix Jones and Amir Bashir

Massey University

**Abstract:** A variety of computationally efficient Bayesian models for the covariance matrix of a multivariate Gaussian distribution are available. However, all produce a relatively dense estimate of the precision matrix, and are therefore unsatisfactory when one wishes to use the precision matrix to consider the conditional independence structure of the data. This talk considers the posterior of model fit for these covariance models. We then undertake post-processing of the Bayes point estimate for the precision matrix to produce a sparse model whose expected fit lies within the upper 95% of the posterior over fits. Extensions to finding sparse differences between inverse covariance matrices are also considered. We illustrate our findings with moderate dimensional data examples from metabolomics.

**Keywords:**Gaussian graphical models, precision matrices, Bayesian models, metabolomics

Wednesday 13^{th} 16:00 Case Room 3 (260-055)

## Dimension Reduction Strategies For Modeling Bi-Clustered High Dimensional Data

Michael Van Supranes and Joseph Ryan Lansangan

University of the Philippines Diliman

**Abstract:**A three-stage framework is developed for fitting a mixture of regressions for high dimensional data. The method combines a hierarchical agglomerative grouping algorithm, regression-based clustering, and a sequential, group-wise sparse estimation called Layered Elastic Net Selection (LENS). A simulation study is used to compare the method with LASSO-type and PC-based strategies in terms of predictive accuracy, selection optimality, and clustering accuracy. All simulation scenarios are high dimensional (n<<p), wherein the best subset of predictors may or may not vary among clusters. When the group of most important predictors varies among regression components, the combination of ordinary least squares (OLS) and LENS for mixture of regressions outperforms LASSO-type and PC-based strategies in terms of prediction and clustering accuracy. Based on simulation, the method (termed as MixLENS) results to optimal variable selection, and applying OLS on selected variables results to better prediction and clusters. OLS-MixLENS may result to a more interpretable model that is as predictive as a full model (e.g. Mixture of PC Regressions). In general, MixLENS is likely to select an optimal small subset of predictors for modeling.

Wednesday 13^{th} 16:00 Case Room 1 (260-005)

## Investigating Methods To Produce Price Indexes From Big Data

Alan Bentley, Mathew Stansfield, and Sam Olivecrona

Stats NZ

**Abstract:** We will present our latest findings on a promising method to use big data for enhancing and improving our current data collections and price measurement. We apply a fixed effects regression approach including using the Fixed Effects Window Splice (FEWS) technique to produce unrevised price indexes at near real-time. We will give examples using daily web scraped food data and administrative rent data.

Stats NZ recently signed up to purchase a trial supply of daily web-scraped online price data from PriceStats, the commercial counterpart of MIT’s Billion Prices Project. This data captures, in real-time, online prices for a wide range of different NZ retailers. Preliminary research on measuring rent price change from government administrative data held by MBIE will also be used to illustrate our approach to the art of using *big data*. This data source highlights the opportunities and obstacles of coverage, timing and quality adjustment.

**References:**

Krsinich, F (2016). The FEWS index: Fixed effects with a window splice. *Journal of Official Statistics*, Vol. 32, No. 2, 2016, pp. 375–404

Wednesday 13^{th} 16:20 098 Lecture Theatre (260-098)

## Computing Entropies With Nested Sampling

Brendon Brewer

University of Auckland

**Abstract:** The Nested Sampling algorithm, invented in the mid-2000s by John Skilling, represented a major advance in Bayesian computation. Whereas Markov Chain Monte Carlo (MCMC) methods are usually effective for sampling posterior distributions, Nested Sampling also calculates the marginal likelihood integral used for model comparison, which is a computationally demanding task. However, there are other kinds of integrals that we might want to compute. Specifically, the entropy, relative entropy, and mutual information, which quantify uncertainty and relevance, are all integrals whose form is inconvenient in most practical applications. I will present my technique, based on Nested Sampling, for estimating these quantities for probability distributions that are only accessible via MCMC sampling. This includes posterior distributions, marginal distributions, and distributions of derived quantities. I will present an example from experimental design, where one wants to optimise the relevance of the data for inference of a parameter.

**Keywords:** Bayesian inference, Nested Sampling, Markov Chain Monte Carlo, Information theory

**References:**

Brewer, B. J. (2017). *Computing Entropies with Nested Sampling.* Entropy, 19, 422.

*Nested Sampling for General Bayesian Computation.*Bayesian analysis, 1(4), 833-859.

Wednesday 13^{th} 16:20 Case Room 4 (260-009)

## Spline-Based Drift Models For High Temperature Operating Life Tests

Vera Hofer and Thomas Nowak

University of Graz

**Abstract:** Since the proper operation of semiconductor devices is of crucial importance for the reliability of a vast range of products, issues concerning quality control are of central relevance to manufacturers. This quality control task is concerned with high temperature operating life tests, where devices are exposed to high temperatures, pressures or humidity, which causes the devices to age artificially fast.

Based on measurements of a random sample of devices, the aim of this work is to compute tolerance limits, such that all subsequent measurements during the stress test stay within their predefined specification limits with a given high probability. These tolerance limits can then be used by automated test equipment for the quality control of devices directly from the production line without their prior exposure to stress test conditions.

In this study, we model the drift behavior of electrical parameters using linear and cubic hermite splines, which are assumed to resemble the true, yet unobserved drift behavior. These spline models allow for the computation of probabilities for an electrical parameter to stay or leave its specification limits at a given point in time. While a very restrictive choice of the tolerance limits might achieve a high level of reliability, the resulting yield loss might get unnecessarily high. Therefore, we formulate an optimization problem that maximizes the probability for initial measurements to be within the tolerance limits (in order to minimize the resulting yield loss) and where the reliability requirement is formulated as a constraint. A derivative-free search algorithm is proposed for this optimization problem, which is then used to test the performance and validity of the model.

**Acknowledgment**

This work was supported by the ECSEL Joint Undertaking under grant agreement No. 662133 - PowerBase. This Joint Undertaking receives support from the European Union’s Horizon 2020 research and innovation programme and Austria, Belgium, Germany, Italy, Netherlands, Norway, Slovakia, Spain and United Kingdom.

**Keywords:**quality control, tolerance limits, splines, reliability engineering

Wednesday 13^{th} 16:20 OGGB5 (260-051)

## A New Approach To Distribution Free Tests In Contingency Tables

Thuong Nguyen

Victoria University of Wellington

**Abstract:** We will discuss in this talk a new construction for a class of distribution free goodness of fit tests for the classical problem: testing independence in contingency tables. The point is that this problem has been stayed with only one asymptotically distribution free goodness of fit test for a long time, the chi-square test. We will show that our class of new distribution free goodness of fit tests is very wide and discuss the cases where the new tests perform better than the conventional chi-square test.

**Keywords:** Contingency tables, distribution free, goodness of fit tests

**References:**

Khmaladze, E., (2013). Note on distribution free testing for discrete distribution, *Annals of Statistics*, **41**, 2979–2993

Khmaladze, E., (2016). Unitary transformations, empirical processes and distribution free testing, *Bernoulli*, **22**, 563–588

*Metrika*,

**80**, 153–170

Wednesday 13^{th} 16:20 Case Room 2 (260-057)

## A Bayesian Inference For Time Series Via Copula-Based Markov Chain Models

Li-Hsien Sun

National Central University

**Abstract:**We study the non-standardized Student’s

*t*-distribution for fitting serially correlated observations where serial dependence is described by the copula-based Markov chain. Due to the computational difficulty of obtaining maximum likelihood estimates, alternatively, we develop Bayes inference using the empirical Bayes method through the resampling procedure. We provide the simulations to examine the performance and also analyze the stock price data in empirical studies for illustration.

Wednesday 13^{th} 16:20 Case Room 3 (260-055)

## Modified Gene Shaving Algorithm - A Dimension REduction And Clustering Method

Donna Mae Santos^{1}, Erniel Barrios^{2}, and Joseph Ryan Lansangan^{2}

^{1}Quirino State University

^{2}University of the Philippines Diliman

**Abstract:** High dimensional data exist in digital images, financial time series and gene expression microarrays. Dealing with high dimensionality has become a challenge, where the difficulty lies on how to visualize and explore the high dimensional function or data set. Gene shaving is a statistical method which is based on Principal Component Analysis (PCA) that has proven its worth in visualization and exploration of microarray data. In this paper, the gene shaving algorithm was modified using PCA and Sparse Principal Component Analysis (SPCA), and the modified algorithms were explored in terms dimension reduction and clustering of variables in a more general (not necessarily microarray) high dimensional data setting.The proposed algorithms were evaluated through a simulation study. Simulation results suggest that the modified algorithms identify a singly cluster of variables that may already best explain the variations in the entire data and/or that already are the most informative. Also, the algorithms may produce overlapping clusters, whose variables in the succeeding clusters (other than the first cluster) are those that may provide information not inherent to the first cluster. The modified algorithms are thus potential and useful for exploration and identification of a group of variables worth for further investigation, as well as clustering/groups of variables for understanding variable structures/relationships.

**Keywords:**High dimensional data, Cluster of Variables, Gene Shaving, Principal Component Analysis, Sparse Principal Component Analysis, Dimension Reduction

Wednesday 13^{th} 16:20 Case Room 1 (260-005)

## The Potential Of Web Scraping

Mathew Stansfield and Sam Olivecrona

Stats NZ

**Abstract:**As part of Stats NZ’s initiative to explore alternative methods of data collection for price indexes we are currently investigating web scraping. In the short term we are looking to substitute manual online collection, in the medium term we are looking to produce a real-time

*Digital Food Price Index*. We will demonstrate a basic technique of web scraping through the R package

`rvest`

. We will discuss some of the challenges and limitations of web scraping more sophisticated websites, and using web scraped data in the production of official price indexes. Some challenging questions in this area are regarding the reliability, relevance, and ethics of using internet prices. Will web scraping make us too reliant on external data sources? Do online prices reflect what consumers pay? Is the publicly available data truly public, or does it belong to the company?

Wednesday 13^{th} 16:40 Case Room 4 (260-009)

## A Simple Method To Construct Confidence Bands In Functional Linear Regression

Masaaki Imaizumi^{1} and Kengo Kato^{2}

^{1}Institute of Statistical Mathematics

^{2}Unversity of Tokyo

**Abstract:**This paper develops a simple method to construct confidence bands, centered at a principal component analysis (PCA) based estimator, for the slope function in a functional linear regression model with a scalar response variable and a functional predictor variable. The PCA- based estimator is a series estimator with estimated basis functions, and so construction of valid confidence bands for it is a non-trivial challenge. We propose a confidence band that aims at covering the slope function at “most” of points with a prespecified probability (level), and prove its asymptotic validity under suitable regularity conditions. Importantly, this is the first paper that derives confidence bands having theoretical justifications for the PCA-based estimator. We also propose a practical method to choose the cut-off level used in PCA-based estimation, and conduct numerical studies to verify the finite sample performance of the proposed confidence band. Finally, we apply our methodology to spectrometric data, and discuss extensions of our methodology to cases where additional vector-valued regressors are present.

Wednesday 13^{th} 16:40 OGGB5 (260-051)

## Separation Of Symmetry For Square Contingency Tables With Ordinal Categories

Kouji Tahata

Tokyo University of Science

**Abstract:** Symmetry and asymmetry models are used to analyze a *square* contingency table with ordinal categories. Caussinus (1966) pointed out that the symmetry model, which indicates the structure of symmetry for cell probabilities, could be separated into the structure of symmetry for odds-ratios and that of symmetry for marginal distributions. This result provides the reason for poor fit of the symmetry model when it occurs for a real dataset. Also, other separations of the symmetry model have been given. For example, Kateri and Agresti (2007), and Saigusa et al. (2015). In this paper, we consider the separation of symmetry by using the generalized asymmetry models. A theorem which the likelihood ratio statistic for testing goodness of fit of the symmetry model is asymptotically equivalent to the sum of those for testing the generalized asymmetry model and the moment equality model under some conditions is given. A simulation study is presented.

**Keywords:** \(f\)-divergence, moment equality, orthogonality, quasi-symmetry

**References:**

Caussinus, H. (1966). Contribution à l’analyse statistique des tableaux de corrélation. *Ann. Fac. Sci. Univ. Toulouse* **29**, 77–182.

Kateri, M. and Agresti, A. (2007). A class of ordinal quasi-symmetry models for square contingency tables. *Statist. Probab. Lett.* **77**, 598–603.

*Statist. Probab. Lett.*

**101**, 33–37.

Wednesday 13^{th} 16:40 Case Room 3 (260-055)

## Testing For Presence Of Clustering Effect In Multilevel Model With High-Dimensional Predictors

Frances Claire San Juan^{1}, Erniel Barrios^{2}, and Joseph Ryan Lansangan^{2}

^{1}Cirrolytix Research Services

^{2}University of the Philippines Diliman

**Abstract:**As big data become more accessible with the boom of data analyzing software, creating value through analytics has grown in demand. Dealing with large data sets in anomaly detection problems, accurate tagging of anomalies is oftentimes lacking and expensive. Unsupervised learning via clustering analysis can be performed to derive labelled data, but used alone, is prone to high false alarm rates. We propose a nonparametric procedure to test presence of clustering effect in a multilevel model with a large set of predictors. Model estimation is done through principal component regression (PCR) and two-way analysis-of-variance (ANOVA), embedded in a backfitting algorithm. Hypothesis test is based on sieve bootstrap. A simulation study showed that the test is effective in detecting high clustering effects, and is optimal when sample size exceeds the number of predictors. The test can be a useful support tool to help address limitations of existing cluster-based methods in anomaly detection.

Wednesday 13^{th} 16:40 Case Room 1 (260-005)

## Towards A Big Data CPI For New Zealand

Alan Bentley

Stats NZ

**Abstract:** In our digital age, what’s the best way to measure inflation? We find an abundance of new data sources, yet these are *found data* in the sense that measuring CPI inflation is a secondary use of the data. Coverage and access become key issues. Automated, scalable, price measurement methods are a must. In this session we take stock and explore the path to a *big data* Consumers Price Index (CPI) for New Zealand.

We discuss the drivers for change and the benefits to a big data approach, reflecting on our early adoption of model-based approaches to price measurement, such as using a hedonic model for second-hand cars, and retail transaction—scanner data—for consumer electronics products (including TVs, computers, digital cameras) in the Consumers Price Index.

We look towards the future by considering the opportunities that are currently in front of us. Notably, we recently signed up to the supply of daily web-scraped online price data from PriceStats, the commercial counterpart of MIT’s Billion Prices Project.

**Keywords:**Big data, multilateral price indexes, model-based inflation measurement