Two-Sample Behrens-Fisher Problems for High-Dimensional Data: A Normal-Reference Based Approach

主讲人：张金廷 新加坡国立大学统计与数据科学系教授

时间：2022年10月21日13：00

地点：腾讯会议 815 7887 2599

举办单位：数理学院

主讲人介绍：张金廷教授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统计与数据科学系终身教授，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。

内容介绍：We propose a normal-reference test for the two-sample Behrens-Fisher problems for high-dimensional data where the data dimension is very large and even much larger than the sample size. It is shown that the null distribution of the test statistic is the same as that of a chi-square-type mixture which is obtained from the test statistic itself when the null hypothesis holds and when the two 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. The asymptotical power of the proposed normal-reference test under a local alternative is established. Two simulation studies demonstrate that in terms of size control, the proposed normal- reference test with the three-cumulant matched χ2-approximation performs well regardless if the data are nearly uncorrelated, moderately correlated, or highly correlated and it performs much better than several existing competitors. A real data example illustrates the proposed normal-reference test.