In this talk, we will investigate limiting spectral properties of high dimensional sample spatial-sign covariance matrices. The populations under study are general enough with possibly known or unknown location vectors, to include the popular independent components model and the family of elliptical distributions. The first result establishes that the empirical spectral distributions of high dimensional sample spatial-sign covariance matrices converge to a deterministic generalized Marcenko-Pastur law. The second result establishes the central limit theorems for a class of linear spectral statistics and we will show for data with known or unknown location vectors, the difference of their CLTs only lies in a mean shift.

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