This paper investigates the spectral properties of spatial-sign covariance matrices, a self-normalized version of sample covariance matrices, for data from $\alpha$-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{\u{c}}enko-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.

翻译：本文研究了空间符号协方差矩阵的谱性质，该矩阵是样本协方差矩阵的自归一化版本，适用于具有一般协方差结构的α-正则变化总体数据。通过利用自归一化随机变量的优良性质，我们建立了极限谱分布及线性谱统计量的中心极限定理。我们证明当α≥2时Marčenko-Pastur方程成立，而线性谱统计量的中心极限定理在α>4时有效，这些条件被证明是相依重尾数据空间符号协方差矩阵近乎最弱的可能条件。