Academic

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. In this talk, I 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, I obtain new multivariate Hájek asymptotic representation results and use them for local power analyses that demonstrate the statistical efficiency of our tests.