学术动态

On structure testing for component covariance matrices of a high-dimensional mixture

报 告 人: 李卫明

报告地点: 数学与统计学院四楼报告厅

报告时间: 2017年02月24日星期五15:30-16:30

报告简介:

By studying the family of p-dimensional scaled mixtures, this paper shows for the first time a non trivial example where the eigenvalue distribution of the corresponding sample covariance matrix does not converge to the celebrated Marcenko-Pastur law. A different and new limit is found and characterized. The reasons of failure of the Marcenko-Pastur limit in this situation are found to be a strong dependence between the p-coordinates of the mixture. Next, we address the problem of testing whether the mixture has a spherical covariance matrix. It is shown that the traditional John’s test and its recent high-dimensional extensions both fail for high-dimensional mixtures, precisely due to the different spectral limit above. In order to find a remedy, we establish a novel and general CLT for linear statistics of eigenvalues of the sample covariance matrix. A new test using this CLT is constructed afterwards for the sphericity hypothesis.

 

主讲人简介:

李卫明博士毕业于东北师范大学,现任教于上海财经大学统计与管理学院;主要研究方向为随机矩阵理论和高维数据分析。

专题网站Project site