Shape of a Distribution Through the L2-Wasserstein Distance

Juan A. Cuesta-Albertos, Carlos Matrán Bea and Jesús M. Rodríguez Rodríguez
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Juan A. Cuesta-Albertos: Universidad de Cantabria, Departamento de Matemáticas
Carlos Matrán Bea: Universidad de Valladolid, Departamento de Estadística e I.O.
Jesús M. Rodríguez Rodríguez: Universidad de Valladolid, Departamento de Estadística e I.O.

A chapter in Distributions With Given Marginals and Statistical Modelling, 2002, pp 51-61 from Springer

Abstract: Abstract Abstract Let Q be a probability measure on ℝ d and let ℑ be a family of probability measures on ℝ d which will be considered as a pattern. For suitable patterns we consider the closest law to Q in ℑ, through the L2-Wasserstein distance, as a descriptive measure associated to Q. The distance between Q and ℑ is a natural measure of the fit of Q to the pattern. We analyze this approach via the consideration of different patterns. Some of them generalize usual location and dispersion measures. Special attention will be paid to patterns based on uniform distributions on suitable families of sets, like the intervals in the unidimensional case (which allows us to analyze the flatness of the one-dimensional distributions) or the ellipsoids for the multivariate distributions.

Keywords: Wasserstein distance; flatness; shape of a distribution; multivariate distributions; Primary 62F05; 62E20; secondary 60F25 (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-0061-0_7

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DOI: 10.1007/978-94-017-0061-0_7

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