题目：Linear Hypothesis Testing in Linear Models with High Dimensional Responses

主讲人：宾州州立大学 李润泽教授

主持人：统计学院 常晋源教授

时间：2021年9月7日（周二）上午10:30-11:30

地点：腾讯会议，423 739 370

报告摘要：

In this paper, we propose a new projection test for linear hypotheses on regression coefficient matrices in linear models with high dimensional responses. We systematically study the theoretical properties of the proposed test. We first derive the optimal projection matrix for any given projection dimension to achieve the best power and provide an upper bound for the optimal dimension of projection matrix. We further provide insights into how to construct the optimal projection matrix. One- and two-sample mean problems can be formulated as special cases of linear hypotheses studied in this paper. We both theoretically and empirically demonstrate that the proposed test can outperform the existing ones for one- and two-sample mean problems. We conduct Monte Carlo simulation to examine the finite sample performance and illustrate the proposed test by a real data example.

主讲人简介：

Runze Li is the Eberly Family Chair in Statistics, the Pennsyvlania State University. His research includes variable selection for high-dimensional data, feature screening for ultrahigh dimensional data, nonparametric and semiparametric regression modeling, and statistical applications to social behavioral science, neural science and engineering. He is a fellow of Institute of Mathematical Statistics, a fellow of American Statistical Association and a fellow of American Association for the Advancement of Science. He received various honors and awards including The United Nations' World Meteorological Organization Gerbier-Mumm International Award for 2012 and ICSA Distinguished Achievement Award in 2017. He served as editor of Annals of Statistics from 2013 to 2015.