A1132
Title: Spectral analysis of spatial-sign covariance matrices for heavy-tailed data with dependence
Authors: Cheng Wang - Shanghai Jiao Tong University (China) [presenting]
Abstract: The spectral properties of spatial-sign covariance matrices, a self-normalized version of sample covariance matrices, are investigated for data from $\alpha$-regularly varying populations with general covariance structures. By exploiting the elegant properties of self-normalized random variables, the limiting spectral distribution and a central limit theorem are established for linear spectral statistics. It is demonstrated that the Marchenko-Pastur equation holds under the condition $\alpha \geq 2$, while the central limit theorem for linear spectral statistics is valid for $\alpha>4$, which are shown to be nearly the weakest possible conditions for spatial-sign covariance matrices from heavy-tailed data in the presence of dependence.
