On eigenvalues of a renormalized sample correlation matrix
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909608606433280 |
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| author | Jiang, Qianqian Zhu, Junpeng Li, Zeng |
| author_facet | Jiang, Qianqian Zhu, Junpeng Li, Zeng |
| contents | This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral statistics. All asymptotic results are derived under a unified framework where the dimension-to-sample size ratio $p/n\rightarrow c\in (0,\infty]$. Based on our CLT result, we propose an independence test statistic capable of operating effectively in both high and ultrahigh dimensional scenarios. Simulation experiments demonstrate the accuracy of theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_08210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On eigenvalues of a renormalized sample correlation matrix Jiang, Qianqian Zhu, Junpeng Li, Zeng Statistics Theory This paper studies the asymptotic spectral properties of a renormalized sample correlation matrix, including the limiting spectral distribution, the properties of largest eigenvalues, and the central limit theorem for linear spectral statistics. All asymptotic results are derived under a unified framework where the dimension-to-sample size ratio $p/n\rightarrow c\in (0,\infty]$. Based on our CLT result, we propose an independence test statistic capable of operating effectively in both high and ultrahigh dimensional scenarios. Simulation experiments demonstrate the accuracy of theoretical results. |
| title | On eigenvalues of a renormalized sample correlation matrix |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2505.08210 |