A Nonparametric Test of Multivariate Independence Using Graphs

Testing whether two sets of variables are correlated is a critical problem in statistical research, and numerous methods have been proposed to address it. However, many existing approaches suffer from various limitations. To overcome these challenges, we propose a graph-based nonparametric strategy that introduces both unweighted and weighted test statistics. To our knowledge, this is the first application of the minimum distance pairing (MDP) graphs in independence testing. The novel method is not susceptible to outliers and applicable in settings where raw data is unavailable due to privacy concerns. We also establish the theoretical properties of the proposed statistics focusing on distributional characteristics and statistical inferences. Extensive numerical studies demonstrate that our approach improves power while maintaining robustness. Finally, a real data analysis further validates its superior performance.