Spectral analysis of spatial-sign covariance matrices for heavy-tailed data with dependence
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917924624662528 |
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| author | Chen, Hantao Wang, Cheng |
| author_facet | Chen, Hantao Wang, Cheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10943 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectral analysis of spatial-sign covariance matrices for heavy-tailed data with dependence Chen, Hantao Wang, Cheng Statistics Theory 62H10, 62E17 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. |
| title | Spectral analysis of spatial-sign covariance matrices for heavy-tailed data with dependence |
| topic | Statistics Theory 62H10, 62E17 |
| url | https://arxiv.org/abs/2502.10943 |