Estimating moments of a selected Pareto population under asymmetric scale invariant loss function
type: Item
instance of: scholarly article
title: Estimating moments of a selected Pareto population under asymmetric scale invariant loss function
zbMATH Open document ID: 1393.62010
author: Riyadh R. Al-Mosawi
author: Shahjahan Khan
published in: Statistical Papers
publication date: 2018-03-22T00:00:00Z
review text: The authors study the problem of estimating moments of the selected (i.\ e., empirically best) out of \(k \geq 2\) Pareto populations possessing the same known shape parameter \(\beta\), but different and unknown scale parameters \(\alpha_i\), \(1 \leq i \leq k\). To this end, they assume that independent random samples of equal size \(n\) from each of the \(k\) populations are available, and they consider an asymmetric scale invariant loss function (ASIL). First, the minimum risk equivariant estimator under ASIL, the uniformly minimum variance unbiased estimator, and the maximum likelihood estimator for \(\alpha_i^t\) are derived, where \(1 \leq i \leq k\) and \(t < \gamma = n \beta\). Three natural estimators \(\delta_E\), \(\delta_U\), and \(\delta_M\) for \(\alpha_{(k)}^t\) (the corresponding moment of the selected population) follow by applying them to the empirically best sample. The authors analyze \(\delta_E\), \(\delta_U\), and \(\delta_M\) with respect to risk-unbiasedness, consistency, and admissibility, and they compare them numerically in a simulation study.
reviewed by: Thorsten Dickhaus
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62F07
Mathematics Subject Classification ID: 62C15
zbMATH DE Number: 6852095
zbMATH Keywords: Pareto distribution
zbMATH Keywords: admissibility
zbMATH Keywords: Brewster-Zidek technique
zbMATH Keywords: estimation following selection
zbMATH Keywords: risk-unbiasedness
MaRDI profile type: Publication
full work available at URL: s00362-016-0758-7
OpenAlex ID: W2279483276
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DOI: 10.1007/S00362-016-0758-7
description: scientific article; zbMATH DE number 6852095