报告人：Runze Li
报告地点：数学与统计学院415室
报告时间：2024年03月15日星期五15:00-16:00
报告摘要：
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.
主讲人简介：
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.
