题目：Normal-Reference Tests for High-Dimensional Hypothesis Testing
报告人：张金廷
会议时间：2025年7月10日(周四) 9: 30
地点：综合楼644会议室
报告人简介：
张金廷教授出生于中国广东省。1988年，他在北京大学获得学士学位，1991年于中国科学院应用数学研究所取得硕士学位，1999年在美国北卡罗来纳大学教堂山分校获得博士学位。张教授曾在哈佛大学从事博士后研究，并先后在普林斯顿大学、罗切斯特大学等多所美国高校担任高级访问学者。
目前，张教授是新加坡国立大学统计与数据科学系的终身教授，并担任博士生和博士后导师。他已培养了10名硕士、10名博士和9名博士后。张教授发表了超过70篇学术论文，撰写了两部统计学专著，并主编了一本学术论文集。他现任或曾任多家学术期刊的副主编或编委，还曾多次参与组织国际大型学术会议。
张金廷教授的研究领域包括非参数统计、纵向数据分析、函数型数据分析和高维数据分析等。
报告摘要：
In the past two decades, much attention has been paid for high-dimensional hypothesis testing. Several centralized or non-centralized L2-norm based test statistics have been proposed. Most of them imposed strong assumptions on the underlying covariance structure of the high-dimensional data so that the associated test statistics are asymptotically normally distributed. In real data analysis, however, these assumptions are hardly checked so that the resulting tests have a size control problem when the required assumptions are not satisfied. To overcome this difficulty, in this talk, we investigate a so-called normal-reference test which can control the size well. In the normal-reference test, the null distribution of a test statistic is approximated with that of a chi-square-type mixture which is obtained from the test statistic when the null hypothesis holds and when the samples are normally distributed. The distribution of the chi-square-type mixture can be well approximated by a three-cumulant matched χ2-approximation with the approximation parameters consistently estimated from the data. Two simulation studies demonstrate that in terms of size control, the proposed normal-reference test performs well regardless of whether the data are nearly uncorrelated, moderately correlated, or highly correlated and it performs much better than two existing competitors. A real data example illustrates the proposed normal-reference test.
