Simple bounds for convergence of empirical and occupation measures in 1-Wasserstein distance

被引:42
|
作者
Boissard, Emmanuel [1 ]
机构
[1] Univ Toulouse 3, Inst Math Toulouse, F-31062 Toulouse, France
来源
关键词
Uniform deviations; Transport inequalities; SMALL BALL PROBABILITIES; WASSERSTEIN DISTANCE; METRIC ENTROPY; QUANTIZATION; THEOREM;
D O I
10.1214/EJP.v16-958
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 study the problem of non-asymptotic deviations between a reference measure mu and its empirical version L-n, in the 1-Wasserstein metric, under the standing assumption that mu satisfies a transport-entropy inequality. We extend some results of F. Bolley, A. Guillin and C. Villani [8] with simple proofs. Our methods are based on concentration inequalities and extend to the general setting of measures on a Polish space. Deviation bounds for the occupation measure of a contracting Markov chain in W-1 distance are also given. Throughout the text, several examples are worked out, including the cases of Gaussian measures on separable Banach spaces, and laws of diffusion processe.
引用
收藏
页码:2296 / 2333
页数:38
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