Admissibility and minimaxity results in the estimation problem of exponential quantiles
type: Item
instance of: scholarly article
title: Admissibility and minimaxity results in the estimation problem of exponential quantiles
zbMATH Open document ID: 0599.62032
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: Let \(X_ 1,X_ 2,...,X_ n\) be a random sample from an exponential distribution with unknown location-scale parameter (\(\xi\),\(\alpha)\) and consider the estimation of the quantiles \(\xi +b\alpha\). The author proves that the traditional estimator (best equivariant) is admissible under quadratic loss when \(n^{-1}\leq b\leq 1+n^{-1}\). Moreover, a class of minimax procedures is found when \(b>1+n^{-1}\). This class is shown to contain generalized Bayes rules and one of them is proved to be admissible within the class of scale-equivariant procedures.
reviewed by: Rasul A. Khan
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62C15
Mathematics Subject Classification ID: 62C20
zbMATH DE Number: 3967667
zbMATH Keywords: admissibility
zbMATH Keywords: exponential distribution
zbMATH Keywords: quantiles
zbMATH Keywords: quadratic loss
zbMATH Keywords: minimax procedures
zbMATH Keywords: generalized Bayes rules
zbMATH Keywords: scale-equivariant procedures
author: Andrew L. Rukhin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349851
OpenAlex ID: W1997880551
DOI: 10.1214/AOS/1176349851
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description: scientific article; zbMATH DE number 3967667