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Activity Number:
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483
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Type:
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Contributed
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Date/Time:
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Thursday, August 7, 2008 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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| Abstract - #302292 |
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Title:
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Admissibility of Generalized Bayes Estimators Through Markov Chain Arguments
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Author(s):
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Brian Shea*+
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Companies:
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The University of Minnesota
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Address:
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313 Ford Hall, Minneapolis, MN, 55455,
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Keywords:
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Admissibility ; Formal Bayes ; Markov chain ; Recurrence ; Multivariate normal distribution
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Abstract:
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Given a parametric model and improper prior distribution, Eaton (1992 {\it Annals}, 1999 {\it PNA}) provided conditions under which recurrence of a Markov chain is a sufficient condition for admissibility of the generalized Bayes estimator under squared error loss. Eaton {\it et al} (2007, {\it Annals} to appear) provide a method of reducing the Markov chain to one dimension as well as moment conditions for the reduced chain's transition kernel that guarantee admissibility. Their results apply to estimating a bounded function of the parameter. We extend these results to the case of estimating unbounded functions of the parameter, and the important special case of estimating the mean of a $p$-dimensional multivariate normal distribution is considered. Generalized Bayes estimators of the mean arising from a class of improper priors are shown to be admissible under squared error loss.
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- Authors who are presenting talks have a * after their name.
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