On a Proper Bayes, but Inadmissible Estimator

Abstract

We present an example of a proper Bayes point estimator which is inadmissible. It occurs for a negative binomial model with shape parameter a, probability parameter p, prior densities of the form π(a,p) = β g(a) (1−p)β−1, and for estimating the population mean μ=a(1−p)/p under squared error loss. Other intriguing features are exhibited such as the constancy of the Bayes estimator with respect to the choice of g, including degenerate or known a cases.