Stein's method for normal approximation in Wasserstein distances with application to the multivariate central limit theorem
成果类型：
Article
署名作者：
Bonis, Thomas
署名单位：
Universite Paris Saclay
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-020-00989-4
发表日期：
2020
页码：
827-860
关键词：
摘要：
We use Stein's method to bound the Wasserstein distance of order 2 between a measure nu and the Gaussian measure using a stochastic process (X-t)(t >= 0) such that X-t is drawn from nu for any t > 0. If the stochastic process (X-t)(t >= 0) satisfies an additional exchangeability assumption, we show it can also be used to obtain bounds onWasserstein distances of any order p >= 1. Using our results, we provide convergence rates for the multi-dimensional central limit theorem in terms of Wasserstein distances of any order p >= 2 under simple moment assumptions.
来源URL：