B0155
Title: Measure-transportation-based quantiles and ranks for directional data
Authors: Thomas Verdebout - Universite Libre de Bruxelles (Belgium) [presenting]
Abstract: Various nonparametric tools for directional data are proposed based on measure transportation. We use optimal transports to define a new notion of cumulative distribution function on the hypersphere together with notions of ranks and signs that are entirely distribution-free. We obtain a closed-form formula for the optimal transport under the classical assumption of rotational symmetry together with a Glivenko-Cantelli result for the empirical version of our cumulative distribution function. We also propose uniformity tests and MANOVA for directions and show that they are asymptotically consistent.
