Markov chain conditions for admissibility in estimation problems with quadratic loss

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.