Concentration Inequalities for Sample Cross-Covariances
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910225636786176 |
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| author | Chen, Jiaheng Sanz-Alonso, Daniel |
| author_facet | Chen, Jiaheng Sanz-Alonso, Daniel |
| contents | This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed by the effective ranks of the two marginal covariance matrices. In the Gaussian case, we prove a matching expectation lower bound, allowing arbitrary correlation between the two random vectors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16733 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Concentration Inequalities for Sample Cross-Covariances Chen, Jiaheng Sanz-Alonso, Daniel Probability Statistics Theory This paper establishes sharp dimension-free concentration and expectation bounds for the deviation of a sample cross-covariance matrix from its mean. For sub-Gaussian random vectors, we prove a high-probability operator-norm bound governed by the effective ranks of the two marginal covariance matrices. In the Gaussian case, we prove a matching expectation lower bound, allowing arbitrary correlation between the two random vectors. |
| title | Concentration Inequalities for Sample Cross-Covariances |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2605.16733 |