数学与统计学院学术报告[2023] 042号

(高水平大学建设系列报告813号)

报告题目: Normal-Reference Tests for High-Dimensional Hypothesis Testing

报告人：张金廷教授（新加坡国立大学）

报告时间： 2023年6月2日（周五） 3:30—4:30

报告地点：汇紫楼B206

报告内容: In the last two decades, there has been significant interest in high-dimensional hypothesis testing, with several centralized or non-centralized L2-norm based test statistics proposed. However, most of these methods rely on strong assumptions about the underlying covariance structure of the data, which are often not checked in real data analysis. As a result, these tests can suffer from size control issues when the assumptions are not satisfied.

To address this problem, this talk introduces a normal-reference test that can effectively control the size of the test. In the normal-reference test, the null distribution of the test statistic is approximated using a chi-square-type mixture derived from the test statistic under the assumption of normality. The distribution of the chi-square-type mixture can be accurately approximated using a three-cumulant matched χ2-approximation, with the approximation parameters estimated from the data.

Simulation studies demonstrate that the proposed normal-reference test performs well in terms of size control, regardless of whether the data are nearly uncorrelated, moderately correlated, or highly correlated, and outperforms two existing competitors. Additionally, a real data example illustrates the effectiveness of the proposed normal-reference test.

报告人简历：

张金廷教授是中国广东省人。1988年在北京大学取得学士学位，1991年在中国科学院应用数学所取得硕士学位， 1999年在美国北卡莱那大学教堂山分校取得博士学位。 张教授曾在哈佛大学做博士后， 并先后在美国普林斯顿，罗泽斯特等大学做高级访问学者。张教授现任新加坡国立大学概率统计系终身教授，博士生，博士后导师。他先后培养了十个硕士，八个博士以及八个博士后。他发表了七十多篇学术论文，撰写了两本统计专著，以及编撰了一本学术论文集。他现任和曾任几家学术期刊的副主编或者编委。他曾是六次大型国际会议的组织成员。张金廷教授现在的研究领域包括非参数统计，纵向数据分析，函数数据分析，高维数据分析，等等。

欢迎师生参加！

报告邀请人：胡宗良      

                                        数学与统计学院

                                     2023年6月2日