Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs

• Activity Number: 79 - Measure Transportation-Based Statistical Inference
• Type: Topic-Contributed
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: IMS
• Author(s): Mathias Drton* and Marc Hallin and Fang Han and Hongjian Shi
• Companies: Technical University of Munich and Université libre de Bruxelles and University of Washington and University of Washington
• Keywords: Multivariate ranks and signs; center-outward ranks and signs; independence test; Hájek representation

Abstract

Rank correlations have found many innovative applications in the last decade. In particular, suitable versions of rank correlations have been used for consistent tests of independence between pairs of random variables. The use of 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. In this talk we will consider the problem of testing independence between two multivariate random vectors and show how the recently introduced concept of center-outward ranks and signs can be used to design consistent and distribution-free tests even in the multivariate case. We will discuss an asymptotic representation of the considered center-outward test statistics under independence, which yields the limiting null distributions for the statistics and facilitates local power analyses.