{"ID":2884810,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.06402","arxiv_id":"2508.06402","title":"Coverage correlation: detecting singular dependencies between random variables","abstract":"We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies 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.","short_abstract":"We introduce the coverage correlation coefficient, a novel nonparametric measure of statistical association designed to quantifies 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 est...","url_abs":"https://arxiv.org/abs/2508.06402","url_pdf":"https://arxiv.org/pdf/2508.06402v2","authors":"[\"Xuzhi Yang\",\"Mona Azadkia\",\"Tengyao Wang\"]","published":"2025-08-08T15:37:18Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"math.ST\"]","methods":"[]","has_code":false}