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arXiv · 2502.10943

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

Hantao Chen·Cheng Wang
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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 Mar{uc}enko-Pastur equation holds under the condition $α\geq 2$, 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.

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Hantao Chen, Cheng Wang. 2025-02-16. Spectral analysis of spatial-sign covariance matrices for heavy-tailed data with dependence. https://arxiv.org/abs/2502.10943

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