The Annals of Statistics

Asymptotically optimal and admissible decision rules in compound compact Gaussian shift experiments

Suman Majumdar

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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.

Article information

Ann. Statist., Volume 24, Number 1 (1996), 196-211.

First available in Project Euclid: 26 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62C25: Compound decision problems
Secondary: 62C15: Admissibility 62E15: Exact distribution theory 62F35: Robustness and adaptive procedures

Compound Bayes rules component Bayes estimator asymptotic optimality admissibility full support hyperprior consistency Gaussian shift experiment qualitative robustness


Majumdar, Suman. Asymptotically optimal and admissible decision rules in compound compact Gaussian shift experiments. Ann. Statist. 24 (1996), no. 1, 196--211. doi:10.1214/aos/1033066206.

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