报告题目：A Correlation-Free Test for High-Dimensional Elliptical Distributions

报告时间：2026年7月21日上午8:00

报告地点：南湖校区综合三报告厅

主办单位：数学与统计学院/科研处

报告人：郭旭

报告人简介：郭旭，现任北京师范大学统计学院教授，博士生导师。曾荣获北京师范大学第十一届“最受本科生欢迎的十佳教师”，北京师范大学第十八届“青教赛”一等奖和北京市第十三届“青教赛”三等奖。目前主要关注高维回归模型中的假设检验问题也对基于机器学习算法的统计推断感兴趣，有多篇文章发表在统计学和计量经济学国际顶尖期刊包括JRSSB, JASA, Biometrika、JOE和JMLR，担任统计学国际知名期刊JMVA副主编。

摘要：Elliptical distributions provide a flexible and widely used extension of multivariate normal distribution. They play a critical role in many statistical procedures when dealing with high-dimensional data. However, goodness-of-fit testing for elliptical distributions remains challenging when the dimension is comparable to or larger than the sample size. In this work, we propose a correlation-free test for high-dimensional elliptical distributions. We establish high-dimensional Gaussian approximation for the test statistic under general correlation structures, allowing the dimension to grow as log p=o(n^{1/14})) under finite moment conditions, without using the inverse sample covariance matrix. We further develop Gaussian multiplier bootstrap test procedure and prove its theoretical validity. Numerical studies demonstrate stable finite-sample behavior and favorable power against a range of alternatives. Applications to real datasets illustrate practical utility of the proposed test.