Estimating normal means with symmetric gain functions
type: Item
instance of: scholarly article
title: Estimating normal means with symmetric gain functions
zbMATH Open document ID: 0638.62027
DOI: 10.1016/0167-7152(87)90050-2
published in: Statistics \& Probability Letters
publication date: 1987-01-01T00:00:00Z
review text: When \(X_ 1,...,X_ n\) are independent and identically distributed normal random variables with unknown mean \(\theta\) and known variance, the estimation problem of \(\theta\) is considered. It is shown that the decision chosen by Bayes rule with a prior density of double exponential type and some symmetric gain function is evaluated in comparison with the sufficient statistic \(\bar X=(X_ 1+...+X_ n)/n\). The above is extended to the case of estimating several means. The previous results by the same author, Stochastic Processes Appl. 14, 267-277 (1983; Zbl 0499.62013); Suppl. Issues Stat. and Decis. 1, 47-59 (1984; Zbl 0558.62025), are involved as special cases.
Mathematics Subject Classification ID: 62F10
Mathematics Subject Classification ID: 62C10
zbMATH DE Number: 4041045
zbMATH Keywords: estimating normal means
zbMATH Keywords: unknown mean
zbMATH Keywords: known variance
zbMATH Keywords: prior density of double exponential type
zbMATH Keywords: symmetric gain function
zbMATH Keywords: sufficient statistic
zbMATH Keywords: estimating several means
author: Lionel Weiss
reviewed by: Masafumi Akahira
MaRDI profile type: Publication
full work available at URL: 0167-7152(87)90050-2
OpenAlex ID: W2061513716
cites work: Small-sample properties of maximum probability estimators
cites work: Q3223691
description: scientific article; zbMATH DE number 4041045