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Uniform priors on convex sets improve risk

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  • Hartigan, J. A.
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    Abstract

    Let X be spherical normal with mean [theta] lying in a closed convex set C with a non-empty interior and a non-empty complement. For the prior distribution uniform over C, the mean squared error risk of the generalized Bayes estimator is less than or equal to that of X for [theta][set membership, variant]C. It is equal to that of X if and only if C is a cone, and [theta] is an apex of the cone.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4BVWSWS-1/2/476796884b7b233f4e76c91f5eef02f5
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 67 (2004)
    Issue (Month): 4 (May)
    Pages: 285-288

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    Handle: RePEc:eee:stapro:v:67:y:2004:i:4:p:285-288

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    Related research

    Keywords: Uniform priors Bayes estimators Squared error loss Improving risk Convex sets Multivariate normal;

    References

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    1. Gatsonis, Constantine & MacGibbon, Brenda & Strawderman, William, 1987. "On the estimation of a restricted normal mean," Statistics & Probability Letters, Elsevier, vol. 6(1), pages 21-30, September.
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    Cited by:
    1. Tatsuya Kubokawa, 2010. "Minimax Estimation of Linear Combinations of Restricted Location Parameters," CIRJE F-Series CIRJE-F-723, CIRJE, Faculty of Economics, University of Tokyo.
    2. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2011. "Modifying estimators of ordered positive parameters under the Stein loss," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 164-181, January.
    3. Tatsuya Kubokawa & �ric Marchand & William E. Strawderman & Jean-Philippe Turcotte, 2012. "Minimaxity in Predictive Density Estimation with Parametric Constraints," CIRJE F-Series CIRJE-F-843, CIRJE, Faculty of Economics, University of Tokyo.
    4. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E. & Turcotte, Jean-Philippe, 2013. "Minimaxity in predictive density estimation with parametric constraints," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 382-397.
    5. Kubokawa, Tatsuya & Strawderman, William E., 2011. "A unified approach to non-minimaxity of sets of linear combinations of restricted location estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1429-1444, November.
    6. Tatsuya Kubokawa & William E. Strawderman, 2010. "Non-minimaxity of Linear Combinations of Restricted Location Estimators and Related Problems," CIRJE F-Series CIRJE-F-749, CIRJE, Faculty of Economics, University of Tokyo.
    7. Tatsuya Kubokawa & William E. Strawderman, 2011. "A Unified Approach to Non-minimaxity of Sets of Linear Combinations of Restricted Location Estimators," CIRJE F-Series CIRJE-F-786, CIRJE, Faculty of Economics, University of Tokyo.

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