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February 1996 Asymptotically optimal and admissible decision rules in compound compact Gaussian shift experiments
Suman Majumdar
Ann. Statist. 24(1): 196-211 (February 1996). DOI: 10.1214/aos/1033066206


Asymptotically optimal and admissible compound decision rules are obtained in a Hilbert-parameterized Gaussian shift experiment. The component parameter set is restricted to compact. For the squared error loss, every compound Bayes estimator is admissible and every compound estimator Bayes versus full support hyperprior mixture of iid priors on the compound parameter is asymptotically optimal. For the latter class of rules induced by full support hyperpriors, asymptotic optimality and admissibility extend to equi- (in decisions) uniformly continuous and bounded risk functions. Normality of certain mixtures of the standard Gaussian process and qualitative robustness of the component Bayes estimator (results of independent interest used in the paper) are derived.


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Suman Majumdar. "Asymptotically optimal and admissible decision rules in compound compact Gaussian shift experiments." Ann. Statist. 24 (1) 196 - 211, February 1996.


Published: February 1996
First available in Project Euclid: 26 September 2002

zbMATH: 0853.62012
MathSciNet: MR1389887
Digital Object Identifier: 10.1214/aos/1033066206

Primary: 62C25
Secondary: 62C15 , 62E15 , 62F35

Keywords: Admissibility , asymptotic optimality , component Bayes estimator , Compound Bayes rules , consistency , full support hyperprior , Gaussian shift experiment , Qualitative robustness

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 1 • February 1996
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