Coverage correlation: detecting singular dependencies between random variables

Fuente: arXiv
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Auteurs principaux: Yang, Xuzhi, Azadkia, Mona, Wang, Tengyao
Format: Preprint
Publié: 2025
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author Yang, Xuzhi
Azadkia, Mona
Wang, Tengyao
author_facet Yang, Xuzhi
Azadkia, Mona
Wang, Tengyao
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_06402
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Coverage correlation: detecting singular dependencies between random variables
Yang, Xuzhi
Azadkia, Mona
Wang, Tengyao
Methodology
Statistics Theory
62H20, 62H15
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.
title Coverage correlation: detecting singular dependencies between random variables
topic Methodology
Statistics Theory
62H20, 62H15
url https://arxiv.org/abs/2508.06402