Independence testing for mixed-type data using distributional transformations

Abstract

The problem of testing independence is addressed in mixed-type data settings where some components are discrete and others are positive and absolutely continuous. Two testing procedures are developed based on the recently introduced Barnighausen-Gaigal transformation, which characterises the joint distribution of such data. The asymptotic properties of the proposed tests are derived, and their practical performance is assessed through an extensive power study, which demonstrates the competitiveness and flexibility of the new approach.