Testing independence between high-dimensional random vectors using rank-based max-sum tests

Wang, Hongfei

doi:10.1111/sjos.70063

Testing independence between high-dimensional random vectors using rank-based max-sum tests

2026-03-01

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DOI：10.1111/sjos.70063

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In this paper, we address the problem of testing independence between two high-dimensional random vectors. Our approach involves a series of max-sum tests based on three well-known classes of rank-based correlations. These correlation classes encompass several popular rank measures, including Spearman's , Kendall's , Hoeffding's D, Blum-Kiefer-Rosenblatt's R, and Bergsma-Dassios-Yanagimoto's . The key advantages of our proposed tests are threefold: (1) they do not rely on specific assumptions about the distribution of random vectors, which makes them applicable across a wide range of settings; (2) they can effectively capture nonlinear dependence structures between random vectors, a critical aspect in high-dimensional contexts; (3) they exhibit robust power performance under both sparse and dense alternatives. Notably, our proposed tests exhibit robust power across a variety of scenarios, as evidenced by extensive numerical results and an empirical application to RNA microarray data.

Keywords:

high dimensionality

independence tests

rank-based correlations

Testing independence between high-dimensional random vectors using rank-based max-sum tests

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