Tusnady's lemma, 24 years later
type: Item
instance of: scholarly article
title: Tusnady's lemma, 24 years later
zbMATH Open document ID: 1016.60037
DOI: 10.1016/S0246-0203(02)01130-5
author: Pascal Massart
published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques
publication date: 2003-03-11T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/77752
review text: As for the coupling between a binomial random variable \(B_n\) with parameter \((n,1/2)\) and a normal random variable \(Y\) the author establishes the following inequality: \[ \left|B_n-{n\over 2}-{\sqrt n\over 2}Y\right |\leq {3\over 4}+ {Y^2\over 8}. \] The constant \(\frac 34\) in the right hand side of the above inequality improves on the constant 1 appearing in Tusnády's original inequality [cf. \textit{J. Bretagnolle} and \textit{P. Massart}, Ann. Probab, 17, No. 1, 239-256 (1989; Zbl 0667.60042)].
Mathematics Subject Classification ID: 60F99
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62G30
zbMATH DE Number: 1879945
zbMATH Keywords: quantile transform
zbMATH Keywords: coupling
zbMATH Keywords: binomial random variable
zbMATH Keywords: normal random variable
reviewed by: Ken-ichi Yoshihara
MaRDI profile type: Publication
Wikidata QID: Q124881309
OpenAlex ID: W2023865454
description: scientific article; zbMATH DE number 1879945