Estimating the quantile function of a location-scale family of distributions based on few selected order statistics
type: Item
instance of: scholarly article
title: Estimating the quantile function of a location-scale family of distributions based on few selected order statistics
zbMATH Open document ID: 0533.62042
DOI: 10.1016/0378-3758(83)90063-0
author: A. K. Md. Ehsanes Saleh
author: M. Masoom Ali
author: Dale Umbach
published in: Journal of Statistical Planning and Inference
publication date: 1983-01-01T00:00:00Z
review text: Let \(X_ 1,...,X_ n\) be i.i.d. random variables with d.f. F where \(F(x)=F_ 0((x-\mu)/\sigma)\) with \(F_ 0\) being a known d.f. and \(\mu\) and \(\sigma\) being unknown location and scale parameters. Given a positive integer k and numbers \(0<p_ 1<p_ 2<...<p_ k<1\) denote by \(X_{(n_ 1)}\leq...\leq X_{(n_ k)}\) the order statistics of \(X_ 1,...,X_ n\) with indices \(n_ i=[np_ i]+1\). By making use of the asymptotic joint normality of \(X_{(n_ 1)},...,X_{(n_ k)}\) one can establish an asymptotically best linear unbiased estimator (ABLUE) of the underlying \(\xi\)-quantile for every fixed vector \((p_ 1,...,p_ k).\) The main purpose of the present article is to find those \(p_ 1,...,p_ k\) which minimize the asymptotic variance over the class of ABLUE's in the particular case of exponential r.v.'s. Further results are obtained for Pareto and double exponential r.v.'s.
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 3846671
zbMATH Keywords: quantile function
zbMATH Keywords: location-scale family
zbMATH Keywords: order statistics
zbMATH Keywords: nonregular distribution
zbMATH Keywords: double exponential distribution
zbMATH Keywords: Pareto distribution
zbMATH Keywords: optimal spacing
zbMATH Keywords: exponential distribution
zbMATH Keywords: asymptotically best linear unbiased estimator
MaRDI profile type: Publication
full work available at URL: 0378-3758(83)90063-0
OpenAlex ID: W2126042854
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description: scientific article; zbMATH DE number 3846671