统计与数据科学系系列学术报告之四百二十一期

时间： 2024年3月18日（周一）16:00-17:00

地点：李达三楼105室

主持人：复旦大学管理学院统计与数据科学系朱仲义教授

报告人：Professor Runze Li The Pennsylvania State University

题目：Tests for shape matrices in moderate dimension via Tyler's M estimators

摘要：Tyler's M estimator, as a robust alternative to the sample covariance matrix, has been widely applied in robust statistics. However, classical theory on Tyler's M estimator is mainly developed in the low-dimensional regime for elliptical populations. It remains largely unknown when the parameter of dimension $p$ grows proportionally to the sample size $n$ for general populations. By utilizing the eigenvalues of Tyler's M estimator, this article develops tests for the identity and equality of shape matrices in a large-dimensional framework where the dimension-to-sample size ratio $p/n$ has a limit in $(0, 1)$. The proposed tests can be applied to a broad class of multivariate distributions including the family of elliptical distributions. To analyze both the null and alternative distributions of the proposed tests, we provide a unified theory on the spectrum of a large-dimensional Tyler's M estimator when the underlying population is general. Simulation results demonstrate good performance and robustness of our tests. An empirical analysis of the Fama-French 49 industrial portfolios is carried out to demonstrate the shape of the portfolios varying.

个人简介：Runze Li is the Eberly Family Chair Professor in Statistics, The Pennsylvania State University. He served as Co-Editor of Annals of Statistics from 2013 to 2015. Runze Li is Fellow of IMS, ASA and AAAS. His recent honors and awards also include the Distinguished Achievement Award of International Chinese Statistical Association, 2017, Faculty Research Recognition Awards for Outstanding Collaborative Research. College of Medicine, Penn State University in 2018 and Distinguished Mentoring Award, Eberly College of Science, Penn State University in 2023. His research interests include theory and methodology in variable selection, feature screening, robust statistics, nonparametric and semiparameteric regression. His interdisciplinary research aims to promote the better use of statistics in social behavioral research, neural science research and climate studies.