Estimating the mean of a normal distribution with loss equal to squared error plus complexity cost
type: Item
instance of: scholarly article
title: Estimating the mean of a normal distribution with loss equal to squared error plus complexity cost
zbMATH Open document ID: 0629.62009
author: Peter J. Kempthorne
published in: The Annals of Statistics
publication date: 1987-01-01T00:00:00Z
review text: Estimating the mean of a p-variate normal distribution is considered when the loss is squared error plus a complexity cost. The complexity of estimates is defined using a partition of the parameter space into sets corresponding to models of different complexity. The model implied by the use of an estimate determines the estimate's complexity cost. Complete classes of estimators are developed which consist of preliminary-test estimators. As is the case when loss is just squared error, the maximum-likelihood estimator is minimax. However, unlike the no-complexity-cost case, the maximum-likelihood estimator is inadmissible even in the case when \(p=1\) or 2.
Mathematics Subject Classification ID: 62C07
Mathematics Subject Classification ID: 62C20
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 4024492
zbMATH Keywords: squared-error loss
zbMATH Keywords: generalized Bayes
zbMATH Keywords: mean
zbMATH Keywords: p-variate normal distribution
zbMATH Keywords: complexity of estimates
zbMATH Keywords: complexity cost
zbMATH Keywords: preliminary-test estimators
zbMATH Keywords: maximum-likelihood estimator
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176350600
OpenAlex ID: W2010005579
DOI: 10.1214/AOS/1176350600
description: scientific article; zbMATH DE number 4024492