On a Proper Bayes, but Inadmissible Estimator

Pankaj Bhagwat and Éric Marchand

The American Statistician, 2020, vol. 74, issue 3, 294-296

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.

Date: 2020
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DOI: 10.1080/00031305.2019.1604432

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