A multivariate CLT for local dependence with \(n^{-1/2}\log n\) rate and applications to multivariate graph related statistics
type: Item
instance of: scholarly article
title: A multivariate CLT for local dependence with \(n^{-1/2}\log n\) rate and applications to multivariate graph related statistics
zbMATH Open document ID: 0859.60019
author: Yosef Rinott
author: Vladimir Rotar
published in: Journal of Multivariate Analysis
publication date: 1996-08-05T00:00:00Z
review text: Let \(X_1,\dots,X_n\) be \(r\)-dimensional random vectors, and define \(W=X_1+\cdots+X_n\). This paper explores the proximity of \(W\) to the standard normal distribution by presenting upper bounds for \(\sup\{|Eh(W)-\int_{\mathbb{R}^d} h(z)\Phi(dx)|: h\in {\mathcal H}\}\), where \(\Phi\) is the standard normal distribution function on \(\mathbb{R}^d\) and \(\mathcal H\) is a class of functions from \(\mathbb{R}^d\) to \(\mathbb{R}\) which obey certain specified properties. These results are applied to statistical problems involving both random and non-random graphs.
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60B12
Mathematics Subject Classification ID: 62H15
Mathematics Subject Classification ID: 05C80
zbMATH DE Number: 892483
zbMATH Keywords: central limit theorem
zbMATH Keywords: dependent random vectors
zbMATH Keywords: random graphs
zbMATH Keywords: Stein's method
zbMATH Keywords: multivariate statistics
zbMATH Keywords: dependency neighborhoods
reviewed by: R. James Tomkins
MaRDI profile type: Publication
full work available at URL: jmva.1996.0017
OpenAlex ID: W2039866483
DOI: 10.1006/JMVA.1996.0017
description: scientific article; zbMATH DE number 892483