A consistent multivariate test of association based on ranks of distances

TL;DR

This paper introduces a new, simple, and powerful multivariate independence test based on ranks of distances, effective across all dimensions and consistent against all types of dependence, with demonstrated strong performance.

Contribution

The paper proposes a novel rank-based multivariate independence test that is consistent against all alternatives and easy to implement, filling a gap in existing methods.

Findings

Test shows high power in simulations

Effective in all dimensions

Simple and easy to implement

Abstract

We are concerned with the detection of associations between random vectors of any dimension. Few tests of independence exist that are consistent against all dependent alternatives. We propose a powerful test that is applicable in all dimensions and is consistent against all alternatives. The test has a simple form and is easy to implement. We demonstrate its good power properties in simulations and on examples.