Spectral Analysis of Spatial-Sign Covariance Matrices with Dependence and Weaker Moment Conditions

This paper investigates the spectral properties of spatial-sign covariance matrices, a self-normalized version of sample covariance matrices, for data from [Formula: see text]-regularly varying populations with general covariance structures. By exploiting the elegant properties of self-normalized random variables, we establish the limiting spectral distribution and a central limit theorem for linear spectral statistics. We demonstrate that the Marc̆enko-Pastur equation holds under the condition [Formula: see text], while the central limit theorem for linear spectral statistics is valid for [Formula: see text], which are shown to be nearly the weakest possible conditions for spatial-sign covariance matrices from heavy-tailed data in the presence of dependence.