Improved rates of convergence for the multivariate central limit theorem in Wasserstein distance
type: Item
instance of: scholarly article
title: Improved rates of convergence for the multivariate central limit theorem in Wasserstein distance
zbMATH Open document ID: 1547.60028
author: Thomas Bonis
published in: Electronic Journal of Probability
publication date: 2024-08-30T00:00:00Z
review text: Let \(W_1,\ldots,W_n\) be independent and centred random variables on \(\mathbb{R}^d\), and \(W=W_1+\cdots+W_n\) their sum having an identity covariance matrix. The author establishes new bounds in the multivariate central limit theorem for \(W\) in Wasserstein distance of order \(p\geq2\) which improve on the rates available in the literature. The author conjectures that this rate is optimal in the case where the \(W_i\) are identically distributed with non-zero third moment, and their measure includes a continuous component. The proofs make use of Stein's method.
reviewed by: Fraser Daly
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62E17
zbMATH DE Number: 7904040
zbMATH Keywords: central limit theorem
zbMATH Keywords: multivariate normal approximation
zbMATH Keywords: \(p\)-Wasserstein distance
zbMATH Keywords: Stein's method
MaRDI profile type: Publication
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DOI: 10.1214/24-EJP1134
description: scientific article; zbMATH DE number 7904040