A0215
Title: Distribution-free tests of multivariate independence based on center-outward signs and ranks
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 distribution-free and consistent tests of independence between random variables. However, it has long remained unclear how one may construct distribution-free yet consistent tests of independence between random vectors since the traditional concept of ranks relies on ordering data and is tied to univariate observations. 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 developed notion of center-outward ranks and signs, a multivariate generalization of traditional ranks. We obtain multivariate extensions of Hajek asymptotic representation and use them to conduct local power analyses that demonstrate the statistical efficiency of our tests. I will also present multivariate extensions of the quadrant, Spearman, Kendall, and van der Waerden tests based on center-outward ranks and signs. A multivariate Chernoff-Savage property is provided to guarantee that, under elliptical generalized Konijn models, the asymptotic relative efficiency of our van der Waerden tests with respect to Wilks' classical (pseudo-)Gaussian procedure is strictly larger than or equal to one.
