Asymptotic properties of linear functions of order statistics
type: Item
instance of: scholarly article
title: Asymptotic properties of linear functions of order statistics
zbMATH Open document ID: 0652.62015
DOI: 10.1016/0378-3758(88)90006-7
author: Cheun-Der Lea
author: Madan L. Puri
published in: Journal of Statistical Planning and Inference
publication date: 1988-01-01T00:00:00Z
review text: Let \(X_{r:n}\) be the r-th order statistic of a sample of size n. Let \(T_ n\) be the arithmetical mean of \(J(r/(n+1))h(X_{r:n})\), where both J(.) and h(.) are some smooth functions (specified in the paper). The authors establish an almost sure approximation to \(T_ n\), from which asymptotic normality and an iterated logarithm theorem are deduced.
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 4064245
zbMATH Keywords: linear functions of order statistics
zbMATH Keywords: almost sure representation
zbMATH Keywords: Wiener process embedding
zbMATH Keywords: invariance principle
zbMATH Keywords: arithmetical mean
zbMATH Keywords: smooth functions
zbMATH Keywords: almost sure approximation
zbMATH Keywords: asymptotic normality
zbMATH Keywords: iterated logarithm theorem
reviewed by: Janos Galambos
MaRDI profile type: Publication
full work available at URL: 0378-3758(88)90006-7
OpenAlex ID: W1973872467
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description: scientific article; zbMATH DE number 4064245