Consider the problem of estimating a parametric function when the loss is quadratic. Given an improper prior distribution, there is a formal Bayes estimator for the parametric function. Associated with the estimation problem and the improper prior is a symmetric Markov chain. It is shown that if the Markov chain is recurrent, then the formal Bayes estimator is admissible. This result is used to provide a new proof of the admissibility of Pitman's estimator of a location parameter in one and two dimensions.

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CWI
CWI. Probability, Networks and Algorithms [PNA]

Eaton, M.L. (1999). Markov chain conditions for admissibility in estimation problems with quadratic loss. CWI. Probability, Networks and Algorithms [PNA]. CWI.