报告题目：Tests based on the Beta matrix for the equality of two high-dimensional covariance matrices

报 告 人：胡江副教授 东北师范大学

报告时间：2019年11月25日15:00-16:00

报告地点：数学楼第一报告厅

报告摘要：

In this talk, I will report some invariant tests based on the modified likelihood ratio test (LRT) and Pillai's trace statistics for the equality of two high-dimensional covariance matrices. It is well-known that the classical log-LRT is not well defined when the dimension is larger than or equal to one of the sample sizes. Or even the log-LRT is well-defined, it is usually perceived as a bad statistic in the high-dimensional cases because of their low powers under some alternatives. In this talk, we will justify the usefulness of the modified log-LRT, and an invariant test that works well in cases where the dimension is larger than the sample sizes. Besides, the test is established under the weakest conditions on the dimensions and the moments of the samples. The asymptotic distribution of the proposed test statistic is also obtained under the null hypothesis. What is more, we also propose a lite version of two modified LRT and modified Pillai's trace statistics, which are all based on random Beta matrix。

报告人简介：

胡江，目前为东北师范大学副教授，博士研究生导师。从事大维随机矩阵方面的教学与研究工作多年,在AOS等杂志发表多篇论文。主持与参与国家自然科学基金面上项目多项。