Title: On universally consistent and fully distribution-free rank tests of vector independence
Authors: Hongjian Shi - Technical University of Munich (Germany) [presenting]
Marc Hallin - Universite Libre de Bruxelles (Belgium)
Mathias Drton - Technical University of Munich (Germany)
Fang Han - University of Washington (United States)
Abstract: Rank correlations have found many innovative applications in the last decade. In particular, suitable rank correlations have been used for consistent and distribution-free tests of independence between pairs of random variables. 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 distribution-free yet consistent tests of independence between random vectors. We will discuss how this problem can be addressed via a general framework for designing multivariate dependence measures and associated test statistics based on the recently introduced concept of center-outward ranks and signs, a multivariate generalization of traditional ranks. In this framework, we obtain new multivariate Hajek asymptotic representation results and use them for local power analyses that demonstrate the statistical efficiency of our tests.