报告题目：Estimating the spectrum of a high dimensional covariance matrix viaanticommuting variables

报告人：文俊

时间：2019年4月28日下午4点

地点：汇贤楼109教室

主办单位：数学科学学院

报告摘要：

LetSp be a p*p sample covariance matrix such that nSp has the Wishart distributionWp(n,∑p) where ∑p is a p*ppopulation covariance matrix. Konwing Sp, we propose a class of estimators forthe spectrum of ∑p. The estimators are derived byessentially minimizing the distance between the empirical Stieltjes transformof Sp and its espectation. The latter is expressed as a double integral over(0,∞)^2 by the supersymmetry method involving Grassmannor anticommuting variables. Under suitable conditions, these estimators areshown to be weakly consistent as p→∞ such that p/ntends to some constant c>0. Simulations indicate that the proposedestimators perform well relative to other state-of-art spectrum estimators.

个人简介：

WenJun received his Ph.D. in Statistics and Applied Probability from theUniversity of Singapore in 2017. Since then, he has served as a postdoctoralresearcher at the Department of Statistics and Applied Probability at theUniversity of Singapore. His main research area is mathematical statistics, andhis research directions include Covariance strategy, Random strategy history,Spatialhistory, Gaussian random fields and so on.