Independence testing: A new approach for mixed-type multivariate data

Abstract

We address the problem of testing independence in mixed-type data settings, where components may be discrete or positive and absolutely continuous, considering both the independence between these vectors, and total independence. The tests are based on an integral and an L² transformation of a special function of the distribution function, introduced by Barnighaus and Gaigall, which effectively characterizes the joint distribution in such complex, multivariate scenarios. The asymptotic properties of the proposed tests are established, and their practical relevance in higher-dimensional contexts is demonstrated through an extensive power study.