Coverage correlation: detecting singular dependencies between random variables

2025/08/08 by Yang, Xuzhi, Azadkia, Mona, Wang, Tengyao
#62H15 #62H20 #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2508.06402

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.

Citations

• A new measure of dependence: Integrated R²
• Association and Independence Test for Random Objects
• A short proof of the Dvoretzky--Kiefer--Wolfowitz--Massart inequality
• Distribution-free tests of multivariate independence based on center-outward quadrant, Spearman, Kendall, and van der Waerden statistics
• Measuring Association on Topological Spaces Using Kernels and Geometric Graphs
• Optimal rates for independence testing via U-statistic permutation tests
• A simple measure of conditional dependence
• A new coefficient of correlation
• Multivariate Rank-based Distribution-free Nonparametric Testing using Measure Transportation
• High dimensional consistent independence testing with maxima of rank correlations
• Nonparametric independence testing via mutual information
• Symmetric Rank Covariances: a Generalised Framework for Nonparametric Measures of Dependence
• Generalized R-squared for Detecting Dependence
• Kernel-based Tests for Joint Independence
• Large-Sample Theory for the Bergsma-Dassios Sign Covariance
• Sensitivity analysis based on Cramér von Mises distance
• Efficient Computation of the Bergsma-Dassios Sign Covariance
• Monge-Kantorovich Depth, Quantiles, Ranks, and Signs
• On the rate of convergence in Wasserstein distance of the empirical\n measure
• The Randomized Dependence Coefficient
• On Testing Independence and Goodness-of-fit in Linear Models
• Measuring and testing dependence by correlation of distances
• Distribution Free Tests of Independence Based on the Sample Distribution Function
• A NEW MEASURE OF RANK CORRELATION
• NOTES ON THE HISTORY OF CORRELATION

Related

• A new correlation coefficient, its orthogonal decomposition and associated tests of independence
• Measures of dependence between random vectors and tests of independence.\n Literature review
• On independence testing using the (partial) distance correlation
• Non-parametric indices of dependence between components for inhomogeneous multivariate random measures and marked sets
• Modeling coskewness with zero correlation and correlation with zero coskewness