# Shun Matsuuramatsuura Lab.

## Associate ProfessorShun Matsuura • Position：Associate Professor

email：matsuura(at)ae.keio.ac.jp

• ### Keywords

Statistics, Statistical Estimation, Multivariate Analysis

### Overview of Research

We study and develop statistical methods, mainly for multivariate analysis. Recent research interests include statistical estimation and hypothesis testing in (1) principal points of multivariate distributions, (2) multivariate regression analysis, and (3) high-dimensional distributions.

### Major Taught Courses

Statistical Analysis, Multivariate Analysis 1

## Research Contents

### (1) Principal Points of Multivariate Distributions

A set of k-principal points of a probability distribution is the discrete approximation of the probability distribution by k points under a quadratic loss function, which generalizes the mean (expectation) of the probability distribution from one point to k points. We study statistical properties and estimation of principal points of multivariate probability distributions.

### (2) Multivariate Regression Analysis

Regression analysis is one of the most common statistical methods for multivariate analysis. In regression analysis, a function is found to fit explanatory variable(s) and response variable(s). It is called multiple regression analysis if the number of explanatory variables is more than one, and called multivariate (and multiple) regression analysis if the number of response variables is also more than one. Recently, we work on developing optimal estimators in a seemingly unrelated regression model which is a statistical model for multivariate regression analysis.

### (3) Statistical Methods for High-Dimensional Distributions

When the number of dimensions (the number of variables) is larger than the sample size, statistical methods for lower dimensions than the sample size often need to be (significantly) modified to work well. We study statistical methods and statistical hypothesis testing for such high-dimensional distributions.

### Recent Research Theme

• Optimal estimation of principal points of multivariate probability distributions with location and scale parameters
• Best equivariant estimators of regression coefficients and error variance-covariance matrix in a seemingly unrelated regression model
• Statistical hypothesis testing procedures for proportional variance-covariance matrices and common principal components model

### Educational Policies

With the recent development of various statistical methods for various types of data, we think that it is important for students to learn theoretical, statistical, and mathematical backgrounds of multivariate analysis, and to improve their abilities to understand how a statistical method is constructed, what assumptions are underlying the method, and what situations and conditions fit the method well (assuring its high precision) and also do not fit the method.