报 告 人： 周旺 教授
新加坡国立大学 博士生导师
报告题目：Block correlation matrix, second order freeness and high-dimensional independence test
报告时间：
报告地点：静远楼1506学术报告厅
主办单位：太阳成集团、科技处
报告摘要：In this talk, we are concerned with the independence test for k high-dimensional sub-vectors of a normal vector, with fixed positive integer k. A natural high-dimensional extension of the classical sample correlation matrix, namely block correlation matrix, is raised for this purpose. We then construct the so-called Schott type statistic as our test statistic, which turns out to be a particular linear spectral statistic of the block correlation matrix. Especially, the test dose not require the sample size to be larger than the total or any partial sum of the dimensions of the k sub-vectors. Interestingly, the limiting behavior of the Schott type statistic can be figured out with the aid of the Free Probability Theory and the Random Matrix Theory. Specifically, we will bring the so-called real second order freeness for Haar distributed orthogonal matrices, into the framework of this high-dimensional testing problem. Simulated results show the effect of the Schott type statistic, in contrast to those of the statistics in the literature is satisfactory. This is joint with Zhigang Bao, Jiang Hu, Guangming Pan.
周旺教授简介：
新加坡国立大学教授，主要研究方向为: random matrices, SLE, high dimensional statistics. 近年来发表有较高学术水平的论文四十多篇。其中在概率统计学方面的国际顶尖杂志Ann. Stat., JASA, Ann. Prob., PTRF, Ann. Appl. Prob.上发表论文十余篇。2012年在新加坡国立大学获得“杰出科学家奖”。他还是IMS会员。