Measure Transportation and Statistical Decision Theory

Marc Hallin

No 2021-04, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: Unlike the real line, the real space, in dimension $dgeq 2$, is not canonically ordered. As a consequence, extending to a multivariate context fundamental univariate statistical tools such as quantiles, signs, and ranks is anything but obvious. Tentative definitions have been proposed in the literature but do not enjoy the basic properties (e.g. distribution-freeness of ranks, their independence with respect to the order statistic, their independence with respect to signs, etc.) they are expected to satisfy. Based on measure transportation ideas, new concepts of distribution and quantile functions, ranks, and signs have been proposed recently that, unlike previous attempts, do satisfy these properties. These ranks, signs, and quantiles have been used, quite successfully, in several inference problems and have triggered, in a short span of time, a number of applications: fully distribution-free testing for multiple-output regression, MANOVA, and VAR models, R-estimation for VARMA parameters, distribution-free testing for vector independence, multiple-output quantile regression, nonlinear independent component analysis, etc.

Keywords: Measure transportation; statistical decision theory (search for similar items in EconPapers)
JEL-codes: C44 (search for similar items in EconPapers)
Pages: 29 p.
Date: 2021-01
New Economics Papers: this item is included in nep-ecm and nep-ore
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