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Uniform priors on convex sets improve risk

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  • Hartigan, J. A.

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.

Suggested Citation

  • Hartigan, J. A., 2004. "Uniform priors on convex sets improve risk," Statistics & Probability Letters, Elsevier, vol. 67(4), pages 285-288, May.
    • Handle: RePEc:eee:stapro:v:67:y:2004:i:4:p:285-288
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    References listed on IDEAS

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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. 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.
    2. Chang, Yuan-Tsung & Matsuda, Takeru & Strawderman, William E., 2019. "A note on improving on a vector of coordinate-wise estimators of non-negative means via shrinkage," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 143-150.
    3. Tsukuma, Hisayuki & Kubokawa, Tatsuya, 2008. "Stein's phenomenon in estimation of means restricted to a polyhedral convex cone," Journal of Multivariate Analysis, Elsevier, vol. 99(1), pages 141-164, January.
    4. Tsukuma Hisayuki, 2009. "Shrinkage estimation in elliptically contoured distribution with restricted parameter space," Statistics & Risk Modeling, De Gruyter, vol. 27(1), pages 25-35, November.
    5. 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.
    6. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman, 2014. "On Predictive Density Estimation for Location Families under Integrated L 2 and L 1 Losses," CIRJE F-Series CIRJE-F-935, CIRJE, Faculty of Economics, University of Tokyo.
    7. Tsukuma, Hisayuki, 2014. "Bayesian estimation of a bounded precision matrix," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 160-172.
    8. 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.
    9. 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.
    10. 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.
    11. Yasuyuki Hamura & Tatsuya Kubokawa, 2022. "Bayesian predictive density estimation with parametric constraints for the exponential distribution with unknown location," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 515-536, May.
    12. 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.
    13. Tatsuya Kubokawa & Éric 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.
    14. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E., 2015. "On predictive density estimation for location families under integrated squared error loss," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 57-74.

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