On Convergence Rates of Spiked Eigenvalue Estimates: A General Study of Global and Local Laws in Sample Covariance Matrices
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909886907940864 |
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| author | Jing, Bing-Yi Li, Weiming Xie, Jiahui Zhang, Yangchun Zhou, Wang |
| author_facet | Jing, Bing-Yi Li, Weiming Xie, Jiahui Zhang, Yangchun Zhou, Wang |
| contents | This paper investigates global and local laws for sample covariance matrices with general growth rates of dimensions. The sample size $N$ and population dimension $M$ can have the same order in logarithm, which implies that their ratio $M/N$ can approach zero, a constant, or infinity. These theories are utilized to determine the convergence rate of spiked eigenvalue estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Convergence Rates of Spiked Eigenvalue Estimates: A General Study of Global and Local Laws in Sample Covariance Matrices Jing, Bing-Yi Li, Weiming Xie, Jiahui Zhang, Yangchun Zhou, Wang Statistics Theory This paper investigates global and local laws for sample covariance matrices with general growth rates of dimensions. The sample size $N$ and population dimension $M$ can have the same order in logarithm, which implies that their ratio $M/N$ can approach zero, a constant, or infinity. These theories are utilized to determine the convergence rate of spiked eigenvalue estimates. |
| title | On Convergence Rates of Spiked Eigenvalue Estimates: A General Study of Global and Local Laws in Sample Covariance Matrices |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2511.02456 |