On the mean speed of convergence of empirical and occupation measures in Wasserstein distance

被引：69

作者：

Boissard, Emmanuel ^{[1
]}

Le Gouic, Thibaut ^{[1
]}

机构：

[1] Univ Toulouse 3, Inst Math Toulouse, CNRS UMR 5219, F-31062 Toulouse, France

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2014年 / 50卷 / 02期

关键词：

Wasserstein metrics; Optimal transportation; Functional quantization; Transportation inequalities; Markov chains; Measure theory; SMALL BALL PROBABILITIES; TRANSPORTATION COST; FUNCTIONAL QUANTIZATION; SHARP ASYMPTOTICS; METRIC ENTROPY; INEQUALITIES; RATES;

D O I：

10.1214/12-AIHP517

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：

In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases. This is notably highlighted in the example of infinite-dimensional Gaussian measures.

引用

页码：539 / 563

页数：25

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