报告题目：Testing equality of two high-dimensional spatial sign covariance matrices

报告人：郑术蓉 教授 东北师范大学

报告时间：2018年8月30日下午3:50-4:50

报告地点：数学楼第一报告厅

主办单位：吉林大学数学学院

报告摘要：This paper is concerned with testing the equality of two high-dimensional spatial sign covariance matrices with applications to testing the proportionality of two high-dimensional covariance matrices. It is interesting that these two testing problems are completely equivalent for the class of elliptically symmetric distributions. This paper develops a new test for testing the equality of two high-dimensional spatial sign covariance matrices based on the Frobenius norm of the difference between two spatial sign covariance matrices. Asymptotic normality of the proposed testing statistic is derived under the null and alternative hypotheses when the dimension and sample sizes both tend to infinity. Moreover, the asymptotic power function is also presented. Simulation studies show that the proposed test performs very well in a wide range of settings and can be allowed to the case of large dimension and small sample sizes.