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 ρ and Chatterjee’s ξ. We uncovered the independence between the max-type test and the sum-type test by deriving their joint distribution. This enables the development of a comprehensive max-sum test that tackles both sparse and dense alternative correlation structures adeptly. Leveraging the asymp-totic 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 has been impressively demonstrated through a diverse range of simulation data and a real-world gene expression dataset, underscoring the effectiveness and practical utility of our proposed method.