“人大数学时间I”第二十二期：张金廷教授
为促进学科交流融合、拓宽师生学术视野、释放科研创新活力，助力人大数学学科走向一流，动漫色情片
设立“人大数学时间”，以专题研讨、高端学术论坛为载体，搭建数学思想充分碰撞、优秀人才不断涌流、创造活力竞相迸发的舞台。“人大数学时间”将持之以恒，久久为功，立志通过交流与创新、提出重大问题，引领数学学科及相关领域的创新与发展，成为对我国数学发展有贡献意义的平台。以下为“人大数学时间I”第二十二期信息：
议程：
时间：6月26日（周四）16：00 张金廷教授报告及其前沿问题探讨
地点：立德楼801
线上：腾讯会议：533-116-832
报告：
题目：Normal-Reference Tests for High-Dimensional Hypothesis Testing
主讲专家：张金廷，新加坡国立大学统计与数据科学系终身教授
Abstract： 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.
KEY WORDS: χ2-type mixtures; high-dimensional data; three-cumulant matched χ2-approximation; two-sample Behrens–Fisher problem.
报告人简介：
张金廷教授出生于中国广东省。1988年于北京大学获得学士学位，1991年于中国科动漫色情片应用数学研究所取得硕士学位，1999年于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，先后培养了10名硕士、10名博士和9名博士后。张教授已发表70余篇学术论文，撰写两部统计学专著，并主编一本学术论文集，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、函数数据分析和高维数据分析等。
