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2019 Behavior of the empirical Wasserstein distance in ${\mathbb R}^d$ under moment conditions
Jérôme Dedecker, Florence Merlevède
Electron. J. Probab. 24: 1-32 (2019). DOI: 10.1214/19-EJP266

Abstract

We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order $p\in [1, \infty )$ between the empirical measure of independent and identically distributed ${\mathbb R}^d$-valued random variables and the common distribution of the variables. We only assume the existence of a (strong or weak) moment of order $rp$ for some $r>1$, and we discuss the optimality of the bounds.

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Jérôme Dedecker. Florence Merlevède. "Behavior of the empirical Wasserstein distance in ${\mathbb R}^d$ under moment conditions." Electron. J. Probab. 24 1 - 32, 2019. https://doi.org/10.1214/19-EJP266

Information

Received: 24 July 2018; Accepted: 14 January 2019; Published: 2019
First available in Project Euclid: 14 February 2019

zbMATH: 1406.60009
MathSciNet: MR3916326
Digital Object Identifier: 10.1214/19-EJP266

Subjects:
Primary: 60B10, 60E15, 60F10, 60F15

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