A complete class theorem for estimating a noncentrality parameter
type: Item
instance of: scholarly article
title: A complete class theorem for estimating a noncentrality parameter
zbMATH Open document ID: 0627.62008
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: The author shows that an admissible estimator \(\delta_ 0\) of the noncentrality parameter \(\theta\) of a noncentral \(\chi^ 2\) distribution which has the property \(R(\theta_ 1\delta_ 0)=O(\theta^ k)\) as \(\theta\to \infty\) for some k must be generalized Bayes. Further, the class of generalized Bayes rules satisfying this condition is complete relative to the class of all rules satisfying it. The result is applied to show inadmissibility of \(\delta_ 0(x)=(x-n)^+\) where n is the number of degrees of freedom. Another application demonstrates inadmissibility of \(\delta_ a(z)=a\{(m-z)z-n\}^+\) (a\(\neq 0)\) as an estimator of the noncentrality parameter of the noncentral F distribution with \(m\geq 5\) and n degrees of freedom.
Mathematics Subject Classification ID: 62C07
Mathematics Subject Classification ID: 62C15
Mathematics Subject Classification ID: 62F10
zbMATH DE Number: 4020186
zbMATH Keywords: noncentral chi-square
zbMATH Keywords: squared error loss
zbMATH Keywords: UMVUE
zbMATH Keywords: admissible estimator
zbMATH Keywords: noncentrality parameter
zbMATH Keywords: generalized Bayes rules
zbMATH Keywords: inadmissibility
zbMATH Keywords: noncentral F distribution
author: Mo-Suk Chow
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350375
OpenAlex ID: W1972203341
DOI: 10.1214/AOS/1176350375
description: scientific article; zbMATH DE number 4020186