A0541
Title: High-dimensional consistent independence testing with maxima of rank correlations
Authors: Mathias Drton - Technical University of Munich (Germany)
Fang Han - University of Washington (United States)
Hongjian Shi - Technical University of Munich (Germany) [presenting]
Abstract: 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, non-monotone relationships, calling for methods that can account for such dependencies. A family of tests is proposed to address this challenge, which is constructed using maxima of pairwise rank correlations that permit consistent assessment of pairwise independence. Built upon a newly developed Cramer-type moderate deviation theorem for degenerate U-statistics, our results cover a variety of rank correlations, including Hoeffdings $D$, Blum-Kiefer-Rosenblatts $R$ and Bergsma-Dassios-Yanagimotos $\tau^*$. The proposed tests are distribution-free in the class of multivariate distributions with continuous margins, implementable without the need for permutation, and are shown to be rate-optimal against sparse alternatives under the Gaussian copula model. As a by-product of the study, an identity between the aforementioned three rank correlation statistics is revealed, hence making a step towards proving a conjecture of Bergsma and Dassios.
