A high-dimensional CLT in W2 distance with near optimal convergence rate

被引：0

作者：

Zhai, Alex ^{[1
]}

机构：

[1] Stanford Univ, Stanford, CA 94305 USA

来源：

PROBABILITY THEORY AND RELATED FIELDS | 2018年 / 170卷 / 3-4期

关键词：

CENTRAL-LIMIT-THEOREM; TRANSPORTATION COST; BOUNDS;

D O I：

10.1007/s00440-017-0771-3

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：

Let X-1, ... , X-n be i.i.d. random vectors in R-d with parallel to X-1 parallel to <= beta. Then, we show that 1/root n (X-1 + ... + X-n) converges to a Gaussian in quadratic transportation (also known as "Kantorovich" or "Wasserstein") distance at a rate of O(root d beta log n/root n), improving a result of Valiant and Valiant. The main feature of our theorem is that the rate of convergence is within log n of optimal for n, d -> infinity.

引用

页码：821 / 845

页数：25

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