Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions

详细信息    查看全文

• 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 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 b281d1d5a8e6b9e67937e7c6c95b5ac""> 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 93b67a"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">e^{-t+βφ(t)} which are not mixtures of normals. The proofs do not rely on boundness or monotonicity of the function r(t) in the representation of the Bayes estimator as .