High dimensional consistent independence testing with maxima of rank correlations

Understand

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 non-linear, non-monotone 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.
• Built upon a newly developed Cram\'{e}r-type moderate deviation theorem for degenerate U-statistics, our results cover a variety of rank correlations including Hoeffding's $D$, Blum-Kiefer-Rosenblatt's $R$, and Bergsma-Dassios-Yanagimoto's $\tau^*$.