Sharp dimension-free Frobenius-norm concentration inequalities for sample moment tensors, with matching two-sided Gaussian estimates and an even/odd parity effect.
Concentration Inequalities for Sample Cross-Covariances
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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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Sharp Frobenius-Norm Concentration for Sample Moment Tensors
Sharp dimension-free Frobenius-norm concentration inequalities for sample moment tensors, with matching two-sided Gaussian estimates and an even/odd parity effect.