Electronic Journal of Probability

Behavior of the empirical Wasserstein distance in ${\mathbb R}^d$ under moment conditions

Jérôme Dedecker and Florence Merlevède

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 6, 32 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1550113245

Digital Object Identifier
doi:10.1214/19-EJP266

Mathematical Reviews number (MathSciNet)
MR3916326

Zentralblatt MATH identifier
1406.60009

Subjects
Primary: 60B10: Convergence of probability measures 60F10: Large deviations 60F15: Strong theorems 60E15: Inequalities; stochastic orderings

Keywords
empirical measure Wasserstein distance independent and identically distributed random variables deviation inequalities moment inequalities almost sure rates of convergence

Rights
Creative Commons Attribution 4.0 International License.

Citation

Dedecker, Jérôme; Merlevède, Florence. Behavior of the empirical Wasserstein distance in ${\mathbb R}^d$ under moment conditions. Electron. J. Probab. 24 (2019), paper no. 6, 32 pp. doi:10.1214/19-EJP266. https://projecteuclid.org/euclid.ejp/1550113245


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