Generalized Bayes minimax estimators of location vectors for spherically symmetric distributions |
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Authors: | Dominique Fourdrinier |
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Institution: | a UMR CNRS 6085, Université de Rouen, LITIS, BP 12, 76801 Saint-Étienne-du-Rouvray, France b Hill Center, Department of Statistics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ 08854, USA |
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Abstract: | Let X∼f(∥x-θ∥2) and let δπ(X) be the generalized Bayes estimator of θ with respect to a spherically symmetric prior, π(∥θ∥2), for loss ∥δ-θ∥2. 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-αtβ and e-αt+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 . |
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Keywords: | primary 62C10 62C20 |
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