Rank-based combination independence tests for high-dimensional data

Abstract

This paper proposes a novel approach to enhance the versatility of the max-sum test in high-dimensional data analysis by combining two distinct rank correlation coefficients: Spearman’s $\rho$ and Chatterjee’s $\xi$. We uncovered the independence between the max-type test and the sum-type test by deriving their joint distribution. This insight enables the development of a comprehensive max-sum test that tackles both sparse and dense alternative correlation structures in an adaptive manner. Leveraging the asymptotic independence between the two coefficients and the intrinsic highlights of two single-coefficient tests, we have strategically implemented Cauchy combination principles to devise a multifunctional testing methodology. This approach can accommodate monotonic and nonmonotonic data types and thus offers a versatile solution to a broad spectrum of analytical requirements. This versatility of our proposed method has been impressively demonstrated through a diverse range of simulation data studies and two real-world data analyses, underscoring its effectiveness and practical utility.