Interpoint-ranking sign covariance for the test of independence

We generalize the sign covariance introduced by Bergsma & Dassios (2014) to multivariate random variables and beyond. The new interpoint-ranking sign covariance is applicable to general types of random objects as long as a meaningful similarity measure can be defined, and it is shown to be zero if and only if the two random variables are independent. The test statistic is a $U$-statistic, whose large-sample behaviour guarantees that the proposed test is consistent against general types of alternatives. Numerical experiments and data analyses demonstrate the superior empirical performance of the proposed method.

Automated summary

This study generalizes the sign covariance introduced by Bergsma & Dassios (2014) to multivariate random variables and beyond. The new interpoint-ranking sign covariance can be applied to various types of random objects as long as a meaningful similarity measure can be defined, and it equals zero if and only if the two random variables are independent. Numerical experiments and data analyses illustrate the superior empirical performance of the proposed method.