Shape of a Distribution Through the L2-Wasserstein Distance

  1. Cuesta-Albertos, Juan A. 1
  2. Bea, Carlos Matrán 1
  3. Rodríguez, Jesús M. Rodríguez 1
  1. 1 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

Livre:
Distributions With Given Marginals and Statistical Modelling

ISBN: 9789048161362,  9789401700610

Année de publication: 2002

Pages: 51-61

Type: Chapitre d'ouvrage

DOI: 10.1007/978-94-017-0061-0_7 GOOGLE SCHOLAR lock_openAccès ouvert editor

Résumé

Abstract Let Q be a probability measure on ℝd and let ℑ be a family of probability measures on ℝd 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.

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