On Bayes estimators with uniform priors on spheres and their comparative performance with maximum likelihood estimators for estimating bounded multivariate normal means

Dominique Fourdrinier and Éric Marchand

Journal of Multivariate Analysis, 2010, vol. 101, issue 6, 1390-1399

Abstract: For independently distributed observables: Xi~N([theta]i,[sigma]2),i=1,...,p, we consider estimating the vector [theta]=([theta]1,...,[theta]p)' with loss ||d-[theta]||2 under the constraint , with known [tau]1,...,[tau]p,[sigma]2,m. In comparing the risk performance of Bayesian estimators [delta][alpha] associated with uniform priors on spheres of radius [alpha] centered at ([tau]1,...,[tau]p) with that of the maximum likelihood estimator , we make use of Stein's unbiased estimate of risk technique, Karlin's sign change arguments, and a conditional risk analysis to obtain for a fixed (m,p) necessary and sufficient conditions on [alpha] for [delta][alpha] to dominate . Large sample determinations of these conditions are provided. Both cases where all such [delta][alpha]'s and cases where no such [delta][alpha]'s dominate are elicited. We establish, as a particular case, that the boundary uniform Bayes estimator [delta]m dominates if and only if m

Keywords: Restricted; parameters; Point; estimation; Squared; error; loss; Dominance; Maximum; likelihood; Bayes; estimators; Multivariate; normal; Unbiased; estimate; of; risk; Sign; changes; Modified; Bessel; functions (search for similar items in EconPapers)
Date: 2010
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