主题：Estimating the spectrum of a high dimensional covariance matrix via anticommuting variables
主讲人：新加坡国立大学文骏博士
主持人：统计学院 林华珍教授
时间：2019年4月26日（星期四）下午3:00-4:00
地点：西南财经大学柳林校区弘远楼408会议室
主办单位：统计研究中心 统计学院 科研处
主讲人简介：
文骏于 2017 年在新加坡国立大学统计与应用概率系获得哲学博士学位，此后至今他留校担任博士后研究员。他的主要研究领域为数理统计，研究方向包括 Covariance matrix estimation, Random matrix theory, Spatial statistics, Gaussian random fields 等。
主要内容：
LetSpbe ap × psample covariance matrix such thatnSphas the Wishart distributionWp(n;Σp) where Σpis ap×ppopulation covariance matrix. KnowingSp, we propose a class of estimators for the spectrum of Σp. The estimators are derived by essentially minimizing the distance between the empirical Stieltjes transform ofSpand its expectation. The latter is expressed as a double integral over (0;∞)2 by the supersymmetry method involving Grassmann or anticommuting variables. Under suitable conditions, these estimators are shown to be weakly consistent asp ->∞such thatp/ntends to some constantc >0. Simulations indicate that the proposed estimators perform well relative to other state-of-the-art spectrum estimators.
