Uniform priors on convex sets improve risk
AbstractLet 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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Bibliographic InfoArticle provided by Elsevier in its journal Statistics & Probability Letters.
Volume (Year): 67 (2004)
Issue (Month): 4 (May)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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- 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.
- 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.
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