Bayes compound and empirical Bayes estimation of the mean of a Gaussian distribution on a Hilbert space
type: Item
instance of: scholarly article
title: Bayes compound and empirical Bayes estimation of the mean of a Gaussian distribution on a Hilbert space
zbMATH Open document ID: 0797.62005
DOI: 10.1016/0047-259X(94)80006-H
author: Suman Majumdar
published in: Journal of Multivariate Analysis
publication date: 1994-10-16T00:00:00Z
review text: The paper studies the problem of finding admissible and asymptotically optimal compound and empirical Bayes rules when the component problem is estimation of the mean of a Gaussian distribution on a real, separable, infinite-dimensional Hilbert space under weighted squared-error-loss. The main result is that when the parameter space is a compact subset of the Hilbert space, a sequence of Bayes compound estimators versus a mixture of i.i.d. priors is asymptotically optimal if the mixing hyperprior has full support. The same result holds in the empirical Bayes formulation as well.
reviewed by: Tamer Başar
Mathematics Subject Classification ID: 62C12
Mathematics Subject Classification ID: 62C25
Mathematics Subject Classification ID: 62C15
zbMATH DE Number: 566958
zbMATH Keywords: asymptotic optimality
zbMATH Keywords: empirical Bayes rules
zbMATH Keywords: estimation of the mean
zbMATH Keywords: Gaussian distribution
zbMATH Keywords: real, separable, infinite-dimensional Hilbert space
zbMATH Keywords: weighted squared-error-loss
zbMATH Keywords: sequence of Bayes compound estimators
zbMATH Keywords: mixture of i.i.d. priors
zbMATH Keywords: mixing hyperprior
zbMATH Keywords: full support
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 566958