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：best365体育官网登录入口

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.