On smoothness conditions and convergence rates in the CLT in Banach spaces
type: Item
instance of: scholarly article
title: On smoothness conditions and convergence rates in the CLT in Banach spaces
zbMATH Open document ID: 0794.60003
DOI: 10.1007/BF01192130
author: Vidmantas Bentkus
author: Friedrich Götze
publication date: 1994-08-15T00:00:00Z
review text: In Banach spaces the rate of convergence in the central limit theorem is of order \(O(n^{-1/2})\) for sets which have `regular' boundaries with respect to the given covariance structure and which are three times differentiable. We show that in infinite-dimensional spaces it is impossible to weaken this differentiability condition in general, whereas in finite-dimensional spaces the assumption of convexity suffices. Similar results hold for the expectation of smooth functionals.
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 569085
zbMATH Keywords: central limit theorem
zbMATH Keywords: rate of convergence
zbMATH Keywords: expectation of smooth functionals
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 569085