题目：High dimensional asymptotics of likelihood ratio tests in the Gaussian sequence model under convex constraints

主讲人：罗格斯大学 韩启阳助理教授

主持人：统计学院 常晋源教授

时间：2021年9月10日（周五）上午10:00-11:00

地点：腾讯会议，662 169 903

报告摘要：

In the Gaussian sequence model $Y=\mu+\xi$, we study the likelihood ratio test (LRT) for testing $H_0: \mu=\mu_0$ versus $H_1: \mu \in K$, where $\mu_0 \in K$, and $K$ is a closed convex set in $\R^n$. In particular, we show that under the null hypothesis, normal approximation holds for the log-likelihood ratio statistic for a general pair $(\mu_0,K)$, in the high dimensional regime where the estimation error of the associated least squares estimator diverges in an appropriate sense. The normal approximation further leads to a precise characterization of the power behavior of the LRT in the high dimensional regime. These characterizations show that the power behavior of the LRT is in general non-uniform with respect to the Euclidean metric, and illustrate the conservative nature of existing minimax optimality and sub-optimality results for the LRT. A variety of examples, including testing in the orthant/circular cone, isotonic regression, Lasso, and testing parametric assumptions versus shape-constrained alternatives, are worked out to demonstrate the versatility of the developed theory. This talk is based on joint work with Yandi Shen(UW, Chicago) and Bodhisattva Sen(Columbia).

主讲人简介：

Qiyang Han is an assistant professor of Statistics at Rutgers University. He received a Ph.D. in Statistics from University of Washington under the supervision of Professor Jon A. Wellner. He is broadly interested in mathematical statistics and high dimensional probability, with a particular focus on empirical process theory and its applications to nonparametric and high dimensional statistics.