Bayes compound and empirical Bayes estimation of the mean of a Gaussian distribution on a Hilbert space

Suman Majumdar

Journal of Multivariate Analysis, 1994, vol. 48, issue 1, 87-106

Abstract: The problem of finding admissible and asymptotically optimal (in the sense of Robbins) compound and empirical Bayes rules is investigated, when the component problem is estimation of the mean of a Gaussian distribution (with a known one-to-one covariance C) on a real separable infinite dimensional Hilbert space H under weighted Squared-Error-Loss. The parameter set is restricted to be a compact subset of the Hilbert space isomorphic to H via C1/2. We note that all Bayes compound estimators in our problem are admissible. Our main result is that those Bayes versus a mixture of i.i.d. priors on the compound parameter are a.o. if the mixing hyperprior has full support. The same result holds in the empirical Bayes formulation as well.

Keywords: Bayes; compound; estimators; asymptotic; optimality; Gaussian; distribution; on; a; Hilbert; space; isonormal; process; mixing; prior (search for similar items in EconPapers)
Date: 1994
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