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arXiv · 2605.16733

Concentration Inequalities for Sample Cross-Covariances

Jiaheng Chen·Daniel Sanz-Alonso
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Abstract

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.

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BibTeXRIS

Jiaheng Chen, Daniel Sanz-Alonso. 2026-05-16. Concentration Inequalities for Sample Cross-Covariances. https://arxiv.org/abs/2605.16733

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