Optimal fixed size confidence procedures for a restricted parameter space
type: Item
instance of: scholarly article
title: Optimal fixed size confidence procedures for a restricted parameter space
zbMATH Open document ID: 0562.62032
author: Mehmet Zeytinoglu
author: Max Mintz
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: Suppose Z is a single observation from \(N(\theta,1),\theta \in \Omega =[- d, d]\). Let A be the action space of the statistician and define a loss function L on \(A\times \Omega\) by \(L(a,\theta)=0\) if \(| a-\theta | \leq e\) and 1 if \(| a-\theta | >e\) where \(e>0\) is given. Minimax admissible Bayes estimators \(\delta^*(Z)\) for \(\theta\) with respect to L are determined. The results are extended to include the case where the sampling distribution has a density function which is unimodal and symmetric about the location parameter. The connection between the minimax rule \(\delta^*\) and an optimal fixed size confidence procedure is obtained by noting that \(C^*(Z) = [\delta^*(Z)-e, \delta^*(Z)+e]\) can be interpreted as a confidence procedure of size 2e which has the highest confidence coefficient equal to \(\inf_{\theta} P_{\theta} \{\theta\in C^*(Z)\}\).
Mathematics Subject Classification ID: 62F25
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 62C10
Mathematics Subject Classification ID: 62C15
zbMATH DE Number: 3896099
zbMATH Keywords: mean of normal random variable
zbMATH Keywords: confidence procedures
zbMATH Keywords: zero-one loss function
zbMATH Keywords: restricted parameter space
zbMATH Keywords: location parameter estimation
zbMATH Keywords: Minimax admissible Bayes estimators
zbMATH Keywords: optimal fixed size confidence procedure
zbMATH Keywords: confidence coefficient
reviewed by: Hariharan K. Iyer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346713
OpenAlex ID: W2056183893
DOI: 10.1214/AOS/1176346713
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description: scientific article; zbMATH DE number 3896099