高斯样本的最优匹配[j]

IF 0.4 4区 数学 Q4 STATISTICS & PROBABILITY
M. Ledoux, Jie-Xiang Zhu
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引用次数: 15

摘要

本文是论文[8,9]的延续,其中讨论了高斯样本的经验测度的最优匹配问题和相关的收敛率。在维数和坎托洛维奇参数的进一步步骤在这里实现,证明,给定 $X_1, \ldots, X_n$ 具有共同分布的标准高斯测度的独立随机变量 $\mu$ on $\mathbb{R}^d$, $d \geq 3$,和 $\mu_n \, = \, \frac 1n \sum_{i=1}^n \delta_{X_i}$ 相关的经验测量, $$ \mathbb{E} \big( \mathrm {W}_p^p (\mu_n , \mu )\big ) \, \approx \, \frac {1}{n^{p/d}} $$ 对于任何 $1\leq p < d$,其中 $\mathrm {W}_p$ 是? $p$-康托罗维奇度规。证据依赖于L. Ambrosio, F. Stra和D. Trevisan在紧凑环境中开发的pde和大众运输方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On optimal matching of Gaussian samples III
This article is a continuation of the papers [8,9] in which the optimal matching problem, and the related rates of convergence of empirical measures for Gaussian samples are addressed. A further step in both the dimensional and Kantorovich parameters is achieved here, proving that, given $X_1, \ldots, X_n$ independent random variables with common distribution the standard Gaussian measure $\mu$ on $\mathbb{R}^d$, $d \geq 3$, and $\mu_n \, = \, \frac 1n \sum_{i=1}^n \delta_{X_i}$ the associated empirical measure, $$ \mathbb{E} \big( \mathrm {W}_p^p (\mu_n , \mu )\big ) \, \approx \, \frac {1}{n^{p/d}} $$ for any $1\leq p < d$, where $\mathrm {W}_p$ is the $p$-th Kantorovich metric. The proof relies on the pde and mass transportation approach developed by L. Ambrosio, F. Stra and D. Trevisan in a compact setting.
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来源期刊
CiteScore
0.70
自引率
0.00%
发文量
0
审稿时长
>12 weeks
期刊介绍: PROBABILITY AND MATHEMATICAL STATISTICS is published by the Kazimierz Urbanik Center for Probability and Mathematical Statistics, and is sponsored jointly by the Faculty of Mathematics and Computer Science of University of Wrocław and the Faculty of Pure and Applied Mathematics of Wrocław University of Science and Technology. The purpose of the journal is to publish original contributions to the theory of probability and mathematical statistics.
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