Behavior of the empirical Wasserstein distance in R under moment conditions

被引：7

作者：

Dedecker, Jerome ^{[1
]}

Merlevede, Florence ^{[2
]}

机构：

[1] Univ Paris 05, Sorbonne Paris Cite, Lab MAP5, UMR 8145, Paris, France

[2] Univ Paris Est, LAMA, UMR 8050, UPEM,CNRS,UPEC, Paris, France

来源：

ELECTRONIC JOURNAL OF PROBABILITY | 2019年 / 24卷

关键词：

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

D O I：

10.1214/19-EJP266

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order p is an element of [1, infinity) between the empirical measure of independent and identically distributed 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.

引用

页数：32

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