A Comparison of the Maximum Likelihood Estimator and the Posterior Mean in the Single-Parameter Case

Abstract

Consider estimation of a scalar parameter θ of a distribution on the basis of a random sample of size n. Possible estimators include the maximum likelihood estimator, _n , and the posterior mean with respect to some prior distribution, _n . In this article n and _n are compared by considering a large-sample version of the Pitman nearness criterion; conditions are given under which _n is preferable to _n in this sense. Several examples are provided that show that comparisons of _n , and _n based on Pitman nearness are often in conflict with comparisons based on mean squared error.

Key Words:

• Asymptotic theory
• Bayes estimates
• Pitman nearness