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Uniform priors on convex sets improve risk

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.
Year of publication:
2004
Authors: Hartigan, J. A.
Published in:
Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 67.2004, 4, p. 285-288
Publisher: Elsevier
Keywords: Uniform priors Bayes estimators Squared error loss Improving risk Convex sets Multivariate normal
Type of publication: Article
Source:
Persistent link: https://www.econbiz.de/10005259323
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