报告题目：On the two-sample Behrens-Fisher problem for high-dimensional data

报告时间：2023年10月29日上午8：00-10：00

报告地点：腾讯会议：857-758-725

摘要：In this paper, we study the limiting distribution of Chen-Qin's test statistic and propose a novel weighted bootstrap test procedure for the high-dimensional two-sample Behrens-Fisher problem.

We first show that the test statistic has an asymptotic null that is a mixture of a chi-square-type mixture distribution and a normal distribution, without imposing either the normal assumption or a factor-like model assumption on the underlying distribution. To gain insight into the asymptotic null distribution of the test statistic, we show that under stronger restrictions on the covariance matrices and the null hypothesis, the test statistic is either asymptotically normal or a chi-square-type mixture distribution. The power properties of the test are evaluated asymptotically under the high-dimensional local and fixed alternative hypothesis. We also derive that the proposed weighted bootstrap test procedure has correct test level asymptotically. Two simulation studies and a real data example show that the new weighted bootstrap procedure significantly outperforms other benchmarks in terms of size control and is comparable in terms of power.

报告人简介：史功明，现为首都经济贸易大学博士后。目前主持首经贸博后基金一项，参加国家自然科学基金2项、国家社科科学基金1项。已在国内外学术刊物上发表论文5篇，其中4篇被SCI检索。研究方向为函数型数据分析、高维检验、分位数回归等。