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Activity Number:
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292
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Type:
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Contributed
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Date/Time:
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Tuesday, August 8, 2006 : 10:30 AM to 12:20 PM
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Sponsor:
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Section on Bayesian Statistical Science
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| Abstract - #306945 |
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Title:
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Admissibility and Minimaxity of Generalized Bayes Estimators for Spherically Symmetric Family
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Author(s):
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Yuzo Maruyama*+ and Akimichi Takemura
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Companies:
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University of Tokyo and University of Tokyo
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Address:
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2875 Osoyoos Crescent, Vancouver, BC, V6T 2G3, Canada
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Keywords:
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minimaxity ; admissibility ; regularly varying function ; decision theory ; harmonic prior ; shrinkage estimation
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Abstract:
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We give a sufficient condition for admissibility of generalized Bayes estimators of the location vector of spherically symmetric distribution under squared error loss. We construct a very useful sequence of smooth proper prior densities approaching the target improper density fast enough for establishing the admissibility based on the method of Blyth. Compared to the known results for the multivariate normal case, our sufficient condition is very tight and is close to being a necessary condition. In particular we establish the admissibility of generalized Bayes estimators with respect to the harmonic prior and priors with slightly heavier tail than the harmonic prior. We also discuss conditions of minimaxity of the generalized Bayes estimator with respect to the harmonic prior.
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