Normal approximations to sums of scores based on occupancy numbers
type: Item
instance of: scholarly article
title: Normal approximations to sums of scores based on occupancy numbers
zbMATH Open document ID: 0584.60031
published in: The Annals of Probability
publication date: 1984-01-01T00:00:00Z
review text: Let \((U_ 1,...,U_ n)\) be a multinomial random vector with parameters \((N;p_ 1,...,p_ n)\) and let \(\{\) C(j,k),\(j\geq 0,k=1,2,...,n\}\) be a set of constants, depending upon N. Define \(S=\sum^{n}_{k=1}C(U_ k,k)\), which is known as the sum of scores based on occupancy numbers. In this paper, the authors proved the asymptotic normality of S as N, \(n\to \infty\), under certain conditions. \textit{C. Morris} [Ann. Stat. 3, 165-188 (1975; Zbl 0305.62013)] established the same result under conditions which neither imply nor are implied by those conditions imposed in this paper. Also, the authors mainly establish the bounds of the rates of this convergence under various conditions.
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 3936090
zbMATH Keywords: central limit theorem
zbMATH Keywords: Berry-Esseen bound
zbMATH Keywords: occupancy numbers
zbMATH Keywords: multinomial sums
author: M. P. Quine
author: John Robinson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993228
OpenAlex ID: W2031331465
DOI: 10.1214/AOP/1176993228
description: scientific article; zbMATH DE number 3936090