A high-dimensional CLT in W2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {W}_2$$\end{document} distance wi
A high-dimensional CLT in W2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {W}_2$$\end{document} distance wi
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DOI：
10.1007/s00440-017-0771-3
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发表时间：
2017-03
影响因子：
2
通讯作者：
Alex Zhai
中科院分区：
文献类型：
--
作者：
Alex Zhai
让我们来看看。随机向量然后，我们证明了$$\开始{aligned} \frac{1}{\sqrt{n}}\left（X_1 + \cdots + X_n\right）\end{aligned}$$以二次运输（也称为“Kantorovich”或“Wasserstein”）距离的速率收敛到高斯，改进了Valiant和Valiant的结果。我们的定理的主要特点是收敛速度是最优的。
Letbe i.i.d. random vectors inwith. Then, we show that $$\begin{aligned} \frac{1}{\sqrt{n}}\left( X_1 + \cdots + X_n\right) \end{aligned}$$converges to a Gaussian in quadratic transportation (also known as “Kantorovich” or “Wasserstein”) distance at a rate of, improving a result of Valiant and Valiant. The main feature of our theorem is that the rate of convergence is withinof optimal for.