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arXiv · 2508.06402

Coverage correlation: detecting singular dependencies between random variables

Xuzhi Yang·Mona Azadkia·Tengyao Wang
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Abstract

We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantify the extent to which two random variables have a joint distribution concentrated on a singular subset with respect to the product of the marginals. Our correlation statistic consistently estimates an $f$-divergence between the joint distribution and the product of the marginals, which is 0 if and only if the variables are independent and 1 if and only if the copula is singular. Using Monge--Kantorovich ranks, the coverage correlation naturally extends to measure association between random vectors. It is distribution-free, admits an analytically tractable asymptotic null distribution, and can be computed efficiently, making it well-suited for detecting complex, potentially nonlinear associations in large-scale pairwise testing.

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Xuzhi Yang, Mona Azadkia, Tengyao Wang. 2025-08-08. Coverage correlation: detecting singular dependencies between random variables. https://arxiv.org/abs/2508.06402

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