主  題：High-dimensional spatial-sign covariance matrix

內容簡介：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.
報告人：周旺    教授    博導

時  間：2017-06-21    13:30

地  點：競慧東樓302室

舉辦單位：理學院  統計科學與大數據研究院