A Graph-Based Framework for Nonparametric Tests of Multivariate Independence

Testing the independence between two sets of variables has long been an important issue and various methods have been proposed. Despite this diversity, a persistent need remains for a nonparametric test that maintains high efficiency across diverse alternatives while demonstrating robustness in various scenarios. To address this gap, we propose a graph-based framework for independence testing that incorporates both weighted and unweighted graph representations. The specific procedure involves two steps: constructing separate graphs for each variable set, and calculating statistics based on the vectorized graph representations. The proposed framework not only expands the application scope of graph-based methods but also provides theoretical properties, ensuring its applicability to data for which only pairwise distances are observed and enhancing its robustness. Simulation studies suggest that the proposed methods effectively control the type I error rates and exhibit higher powers than the competing methods. Applications to two real datasets further illustrate the efficiency of the proposed framework. Supplementary materials for this article are available online.