IMPROVING BAYESIAN ESTIMATION OF THE END POINT OF A DISTRIBUTION

Abstract

Bayesian estimation of the end point of a distribution is proposed and examined. For this problem, it is well known that the maximum likelihood method does not work well. By modifying the prior density in Hall and Wang (2005) and applying marginal inference, we derive estimators superior to existing ones. The proposed estimators are closely related to the estimating functions which are known to outperform maximum likelihood equations. Another advantage of the proposed method is to resolve the convergence problem. Our simulation results strongly support the superiority of the proposed estimators over the existing ones under the mean squared error. Illustrative examples are also given.