On spectral properties of high-dimensional spatial-sign covariance matrices in elliptical distributions with applications.
报 告 人:: 李卫明
报告地点:: 数学与统计学院403室
报告时间:: 2017年07月21日星期四16:00-17:00

Spatial-sign covariance matrix (SSCM) is an important substitute of sam-ple covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations, where both the dimension p of observations and the sample size n tend to infinity with their ratio p/n->c>0. The empirical spectral distribution of this nonparametric scatter matrix is shown to converge in distribution to a generalized Marcenko-Pastur law. Beyond this, a new central limit theorem (CLT) for general linear spectral statistics of the SSCM is also established. For polynomial spectral statistics, explicit formulae of the limiting mean and covarance functions in the CLT are provided. The derived results are then applied to an estimation procedure and a test procedure for the spectrum of the shape component of population covariance matrices.

发 布 人:科研助理 发布时间: 2017-07-21
李卫明博士毕业于东北师范大学,现任教于上海财经大学统计与管理学院;主要研究方向为随机矩阵理论和高维数据分析。目前担任Annals of Statistics, Bernoulli, Journal of Multivariate analysis 等杂志审稿人。