威斯康星大学张春明教授系列学术报告1

报告题目：On simultaneous calibration of two-sample t-tests for high-dimension low-sample-size data

报 告 人：Chunming Zhang, Professor of Statistics, University of Wisconsin-Madison

照片：

邀 请 人：冶 继 民 教 授

报告时间：2020年6月10号上午9:00:-10:30

报告平台：Zoom ID:865 6191 9897（密码2ArL1w）

报告人简介：张春明，美国威斯康星大学国际著名统计学教授，统计学四大顶级期刊之一Annals of Statistics的前副主编、Journal of the American Statistical Association的的现任副主编。在统计学四大顶级期刊发表论文10余篇，主要研究领域有：Statistical learning & data mining；Statistical methods with applications to imaging neuroinformatics and bioinformatics；Multiple testing; large-scale simultaneous inference and applications；Statistical methods in financial econometrics；Non- and semi-parametric estimation & inference；Functional & longitudinal data analysis.

报告摘要：Two-sample t-tests have been widely used in research practice and applications. This paper addresses new issues in simultaneously calibrating a diverging number m of two-sample t-statistics for simultaneous inference of significance in high-dimension low-sample size data. For the Gaussian calibration method, we demonstrate that (a) the simultaneous "general" two-sample t-statistics achieve the overall significance level, if log(m) increases at a strictly slower rate than (n_1+n_2)^{1/3} as n_1+n_2 diverges; (b) however, directly applying the same calibration method to simultaneous "pooled" two-sample t-statistics may substantially lose the overall level accuracy. The proposed "adaptively pooled" two-sample t-statistics overcome such incoherence, whereas operate as simply as but perform as well as the "general" two-sample t-statistics. (c) Moreover, we propose a "two-stage" t-test procedure to effectively alleviate the skewness effects commonly encountered from various two-sample t-statistics in practice, thus enhancing the calibration accuracy. Implications of these results are illustrated using simulation studies and real-data applications.