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Monge-Kantorovich Depth, Quantiles, Ranks and Signs

Victor Chernozhukov, Alfred Galichon, Marc Hallin () and Marc Henry

No ECARES 2015-02, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: We propose new concepts of statistical depth, multivariate quantiles,ranks and signs, based on canonical transportation maps between a distributionof interest on IRd and a reference distribution on the d-dimensionalunit ball. The new depth concept, called Monge-Kantorovich depth, specializesto halfspace depth in the case of elliptical distributions, but, for more generaldistributions, differs from the latter in the ability for its contours to account fornon convex features of the distribution of interest. We propose empirical counterpartsto the population versions of those Monge-Kantorovich depth contours,quantiles, ranks and signs, and show their consistency by establishing a uniformconvergence property for transport maps, which is of independent interest.

Keywords: statictical depth; vector quantiles; vector ranks; multivariate signs; optimal transport maps (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2015-01
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Related works:
Working Paper: Monge-Kantorovich Depth, Quantiles, Ranks, and Signs (2015) Downloads
Working Paper: Monge-Kantorovich depth, quantiles, ranks and signs (2015) Downloads
Working Paper: Monge-Kantorovich depth, quantiles, ranks and signs (2015) Downloads
Working Paper: Monge-Kantorovich Depth, Quantiles, Ranks, and Signs (2015) Downloads
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