Distribution-Free Consistent Tests of Independence via Marginal and Multivariate Ranks

Abstract

Testing independence is a fundamental statistical problem that has received much attention in literature. In this dissertation, we consider testing independence under two different settings. The first is testing mutual independence of many covariates, and the second is testing independence of two random vectors. For both settings, we propose, for the first time, distribution-free and consistent tests of independence via marginal or multivariate ranks. Moreover, we establish the optimal efficiency in the statistical sense of both tests. In addition, we also investigate the power of a simple consistent rank correlation coefficient recently proposed by Chatterjee (2021+) against local alternatives. Our results show that Chatterjee's coefficient is unfortunately statistically inefficient.