報告題目：Tests based on the Beta matrix for the equality of two high-dimensional covariance matrices
報 告 人：胡江副教授 東北師範大學
報告時間：2019年11月25日15:00-16:00
報告地點：數學樓第一報告廳
報告摘要：
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。
報告人簡介：
胡江，目前為東北師範大學副教授，博士研究生導師。從事大維随機矩陣方面的教學與研究工作多年,在AOS等雜志發表多篇論文。主持與參與國家自然科學基金面上項目多項。
