Approximation to probabilities through uniform laws on convex sets
type: Item
instance of: scholarly article
title: Approximation to probabilities through uniform laws on convex sets
zbMATH Open document ID: 1025.60009
DOI: 10.1023/A:1023518526754
published in: Journal of Theoretical Probability
publication date: 2003-08-06T00:00:00Z
review text: Consider a probability distribution \(P\) on \(\mathbb{R}^d\), \(d\geq 1\), and denote by \({\mathcal C}\) the family of uniform probabilities supported by compact convex subsets of \(\mathbb{R}^d\) with non-empty interior. Under suitable assumptions, it is proved that there exists a best approximation to \(P\) in \({\mathcal C}\) according to the \(L_2\)-Wasserstein distance. This approximation can be considered as the best representation of \(P\) by a convex set in the minimum squares setting, which improves on other existing representations for the shape of a distribution. As a by-product, the authors derive properties related to the limit behaviour and marginals of uniform probabilities on convex subsets of \(\mathbb{R}^d\).
Mathematics Subject Classification ID: 60E99
Mathematics Subject Classification ID: 52A27
zbMATH DE Number: 1960098
zbMATH Keywords: Wasserstein distance
zbMATH Keywords: uniform laws
zbMATH Keywords: convex sets
zbMATH Keywords: existence
author: Juan Antonio Cuesta-Albertos
author: Carlos Matrán
author: Jesús M. Rodríguez-Rodríguez
reviewed by: Marius Iosifescu
MaRDI profile type: Publication
full work available at URL: a:1023518526754
OpenAlex ID: W151658032
description: scientific article; zbMATH DE number 1960098