Coverage correlation: detecting singular dependencies between random variables
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916901121163264 |
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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 |