High-dimensional spatial-sign covariance matrix-周旺 (新加坡国立大学)

主  题:High-dimensional spatial-sign covariance matrix

内容简介:Spatial-sign covariance matrix (SSCM) is an important substitute  of sample covariance matrix (SCM) in robust statistics.In this talk I will discuss 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 $p/n\to c\in (0, \infty)$. The empirical spectral distribution of this nonparametric scatter matrix is shown to converge in distribution to a generalized Mar\v{c}enko-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.
报告人:周旺    教授    博导

时  间:2017-06-21    13:30

地  点:竞慧东楼302室

举办单位:理学院  统计科学与大数据研究院