Independence Testing for Mixed Data

TL;DR

This paper develops new statistical tests for independence in mixed data types, including count and continuous variables, extending to multivariate cases with theoretical properties and demonstrated effectiveness.

Contribution

Introduces novel independence tests for mixed data types using Baringhaus-Gaigall transformation, applicable to multivariate settings with proven asymptotic properties.

Findings

Tests are asymptotically valid and consistent.

Proposed methods show competitive power in simulations.

Flexible approach applicable to various multivariate mixed data scenarios.

Abstract

We consider the problem of testing independence in mixed-type data that combine count variables with positive, absolutely continuous variables. We first introduce two distinct classes of test statistics in the bivariate setting, designed to test independence between the components of a bivariate mixed-type vector. These statistics are then extended to the multivariate context to accommodate: (i) testing independence between vectors of different types and possibly different dimensions, and (ii) testing total independence among all components of vectors with different types. The construction is based on the recently introduced Baringhaus-Gaigall transformation, which characterizes the joint distribution of such data. We establish the asymptotic properties of the resulting tests and, through an extensive power study, demonstrate that the proposed approach is both competitive and flexible.