【主题】A simple two-sample test in high dimensions

【报告人】Ming-Yen CHENG, 教授

Hong Kong Baptist University

【时间】 2019年7月11日（星期四）09:00-10:00

【地点】上海财经大学统计与管理学院大楼1208会议室

【摘要】Testing the equality of two means is a fundamental inference problem. For high-dimensional data, the Hotelling's T-square test either performs poorly or becomes inapplicable. Several modifications have been proposed to address this issue. However, most of them are based on asymptotic normality of the null distributions of their test statistics which inevitably requires strong assumptions on the covariance matrix. We study this problem thoroughly and propose an L2-norm based test that works under mild conditions and even when there are fewer observations than the dimension. Specifically, to cope with general non-normality of the null distribution we employ the Welch-Satterthwaite chi-square approximation. We derive a sharp upper bound on the approximation error and use it to justify that the chi-squareapproximation is preferred to normal approximation. Simple ratio-consistent estimators for the parameters in the chi-squareapproximation are given. Importantly, our test can cope with singularity or near singularity of the unknown covariance which is commonly seen in high dimensions and is the main cause of non-normality. The power of the proposed test is also investigated. Extensive simulation studies and an application show that our testoutperforms several existing tests in terms of size control, and the powers are comparable when their sizes are comparable.

【嘉宾简介】Dr. Cheng is Professor in Department of Mathematics at Hong Kong Baptist University.  Her research interests include semiparametric and nonparametric modeling, clustering/classification/discrimination, image analysis, change-point analysis, financial time series, high dimensional data and functional data analysis. 

【主持人】黄涛