Proposition and validation of multivariate tests of independence between two groups of variables

Abstract

A commonly used test for the independence of two sets of variables from a normal multivariate population is the Wilks Lambda test or the multivariate likelihood ratio test (LRT). However, this test’s performance is highly influenced by outliers and non-normality of the data and thus, robust test statistics should be used, allied to Monte-Carlo methods. In this paper, we proposed and evaluated three new likelihood ratio test for the independence of two sets of multivariate variables (LRTR, T and TR), replacing the traditional covariance matrix estimator with the robust comedian estimators. The results showed that the proposed test T and TR control type I error rates also for non-normal distributions outperforming the ordinary test.