Abstract

This paper aims to develop an effective model-free inference procedure for high-dimensional data. We first reformulate the hypothesis testing problem via sufficient dimension reduction framework. With the aid of new reformulation, we propose a new test statistic and show that its asymptotic distribution is $\chi^2$ distribution whose degree of freedom does not depend on the unknown population distribution. We further conduct power analysis under local alternative hypotheses. In addition, we study how to control the false discovery rate of the proposed $\chi^2$ tests, which are correlated, to identify important predictors under a model-free framework. To this end, we propose a multiple testing procedure and establish its theoretical guarantees. Monte Carlo simulation studies are conducted to assess the performance of the proposed tests and an empirical analysis of a real-world data set is used to illustrate the proposed methodology.

报告人简介

郭旭博士，现为北京师范大学统计学院教授，博士生导师。郭老师一直从事回归分析中复杂假设检验的理论方法及应用研究，近年来皆在对高维数据发展适当有效的检验方法。部分成果发表在JRSSB, JASA，Biometrika和JOE。担任《应用概率统计》杂志第十届编委。现主持国家自然科学基金优秀青年基金。曾荣获北师大第十一届“最受本科生欢迎的十佳教师”，北师大第十八届青教赛一等奖和北京市第十三届青教赛三等奖。