Testing independence of random vectors by inverse regressions

Abstract

We propose a new test of independence of random vectors. We first show that the null hypothesis implies the nullity of the trace of an operator involving inverse regressions covariance operators. Then, using an approach based on slicing, we define a test statistic for which an asymptotic distribution under null hypothesis is derived. Simulations that permit to evaluate the performance of the proposed test with comparisons with existing methods are given.