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

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  • Fourdrinier, Dominique
  • Marchand, Éric

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

Suggested Citation

  • Fourdrinier, Dominique & Marchand, Éric, 2010. "On Bayes estimators with uniform priors on spheres and their comparative performance with maximum likelihood estimators for estimating bounded multivariate normal means," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1390-1399, July.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:6:p:1390-1399
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    References listed on IDEAS

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    1. Robert, Christian, 1990. "Modified Bessel functions and their applications in probability and statistics," Statistics & Probability Letters, Elsevier, vol. 9(2), pages 155-161, February.
    2. Marchand, Éric & Perron, François, 2002. "On the minimax estimator of a bounded normal mean," Statistics & Probability Letters, Elsevier, vol. 58(4), pages 327-333, July.
    3. Berry, J. Calvin, 1990. "Minimax estimation of a bounded normal mean vector," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 130-139, October.
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