Spectral analysis of spatial-sign covariance matrices for heavy-tailed data with dependence

2025/02/16 by Chen, Hantao, Wang, Cheng
#62E17 #62H10 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2502.10943

Abstract

This paper investigates the spectral properties of spatial-sign covariance matrices, a self-normalized version of sample covariance matrices, for data from α-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 Marucenko-Pastur equation holds under the condition α≥ 2, while the central limit theorem for linear spectral statistics is valid for α>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.

Related

• On eigenvalues of a high-dimensional spatial-sign covariance matrix
• On spectral properties of high-dimensional spatial-sign covariance matrices in elliptical distributions with applications
• CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data
• Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications
• CLT for LSS of sample covariance matrices with unbounded dispersions