High dimensional independence testing with maxima of rank correlations

12/14/2018
by   Mathias Drton, et al.
0

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 Cramér-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 τ^*. The proposed tests are distribution-free, 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, we reveal an identity between the aforementioned three rank correlation statistics, and hence make a step towards proving a conjecture of Bergsma and Dassios.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
04/18/2022

Rank Based Tests for High Dimensional White Noise

The development of high-dimensional white noise test is important in bot...
research
12/28/2021

Rank-1 Similarity Matrix Decomposition For Modeling Changes in Antivirus Consensus Through Time

Although groups of strongly correlated antivirus engines are known to ex...
research
09/15/2023

Fisher's combined probability test for cross-sectional independence in panel data models with serial correlation

Testing cross-sectional independence in panel data models is of fundamen...
research
07/04/2020

Rate-optimality of consistent distribution-free tests of independence based on center-outward ranks and signs

Rank correlations have found many innovative applications in the last de...
research
08/26/2020

On the power of Chatterjee rank correlation

Chatterjee (2020) introduced a simple new rank correlation coefficient t...
research
10/06/2018

Adaptive Independence Tests with Geo-Topological Transformation

Testing two potentially multivariate variables for statistical dependenc...
research
04/18/2023

Independence testing for inhomogeneous random graphs

Testing for independence between graphs is a problem that arises natural...

Please sign up or login with your details

Forgot password? Click here to reset