par Chernozhukov, Victor;Galichon, Alfred;Hallin, Marc ;Henry, Marc
Référence Annals of statistics
Publication A Paraître, 2016
Référence Annals of statistics
Publication A Paraître, 2016
Article révisé par les pairs
Résumé : | We propose new concepts of statistical depth, multivariate quantiles, vector quantiles and ranks, ranks and signs, based on canonical transportation maps between a distribution of interest on Rd and a reference distribution on the d-dimensional unit ball. The new depth concept, called Monge- Kantorovich depth, specializes to halfspace depth for d = 1 and in the case of spherical distributions, but for more general distributions, differs from the latter in the ability for its contours to account for non-convex features of the distribution of interest. We propose empirical counterparts to the population versions of those Monge-Kantorovich depth contours, quantiles, ranks, signs and vector quantiles and ranks, and show their consistency by establishing a uniform convergence property for empirical (forward and reverse) transport maps, which is the main theoretical result of this paper. |