Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions

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• 作者：Dominique Fourdrinier ; William E. Strawderman
• 关键词：Minimax estimators ; Bayes estimators ; Quadratic loss ; Spherically symmetric distributions ; Location parameter ; Superharmonic priors
• 刊名：Journal of Multivariate Analysis
• 出版年：2008
• 出版时间：April 2008
• 年：2008
• 卷：99
• 期：4
• 页码：735-750
• 全文大小：192 K

文摘

Let 4NFR52V-2&_mathId=mml1&_user=1067359&_cdi=6901&_rdoc=10&_acct=C000050221&_version=1&_userid=10&md5=7d9ad619a79a88708360a933533f3c6b"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">Xf(x-θ²) and let δ_π(X) be the generalized Bayes estimator of θ with respect to a spherically symmetric prior, π(θ²), for loss δ-θ². We show that if π(t) is superharmonic, non-increasing, and has a non-decreasing Laplacian, then the generalized Bayes estimator is minimax and dominates the usual minimax estimator δ₀(X)=X under certain conditions on . The class of priors includes priors of the form for and hence includes the fundamental harmonic prior . The class of sampling distributions includes certain variance mixtures of normals and other functions f(t) of the form e^-tβ and e^-t+βφ(t) which are not mixtures of normals. The proofs do not rely on boundness or monotonicity of the function d321a23d9b3246c9f38"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">r(t) in the representation of the Bayes estimator as .