Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916657557929984 |
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| author | Oriol, Benoit |
| author_facet | Oriol, Benoit |
| contents | We compute asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators for weighted sample covariances, and the joint sample-population eigenvector overlap distribution, in the spirit of Ledoit and Péché. We detail explicitly the formulas for exponentially-weighted sample covariances. We propose an algorithm to numerically compute those formulas. Experimentally, we show the performance of the asymptotic non-linear shrinkage estimators. Finally, we test the robustness of the theory to a heavy-tailed distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14420 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance Oriol, Benoit Statistics Theory Machine Learning Probability Applications We compute asymptotic non-linear shrinkage formulas for covariance and precision matrix estimators for weighted sample covariances, and the joint sample-population eigenvector overlap distribution, in the spirit of Ledoit and Péché. We detail explicitly the formulas for exponentially-weighted sample covariances. We propose an algorithm to numerically compute those formulas. Experimentally, we show the performance of the asymptotic non-linear shrinkage estimators. Finally, we test the robustness of the theory to a heavy-tailed distributions. |
| title | Asymptotic non-linear shrinkage and eigenvector overlap for weighted sample covariance |
| topic | Statistics Theory Machine Learning Probability Applications |
| url | https://arxiv.org/abs/2410.14420 |