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随机向量独立性的普遍一致、完全分布自由秩检验AI 解读

Rank correlations have found many innovative applications in the last decade. In particular, suitable rank correlations have been used for consistent tests of independence between pairs of random variables. Using ranks is especially appealing for continuous data as tests become distribution-free. However, the traditional concept of ranks relies on ordering data and is, thus, tied to univariate observations. As a result, it has long remained unclear how one may construct…

基于中心向外秩与符号的分布无关一致独立性检验AI 解读

This article investigates the problem of testing independence of two random vectors of general dimensions. For this, we give for the first time a distribution-free consistent test. Our approach combines distance covariance with the center-outward ranks and signs developed by Marc Hallin and collaborators. In technical terms, the proposed test is consistent and distribution-free in the family of multivariate distributions with nonvanishing (Lebesgue) probability densities.…

基于秩相关最大值的高维一致独立性检验AI 解读

Testing mutual independence for high-dimensional observations is a fundamental statistical challenge. Popular tests based on linear and simple rank correlations are known to be incapable of detecting nonlinear, nonmonotone relationships, calling for methods that can account for such dependences. To address this challenge, we propose a family of tests that are constructed using maxima of pairwise rank correlations that permit consistent assessment of pairwise independence.…