Empirical Bayes Estimation for Uniform Distributions with Random Right Censoring

This article deals with the empirical Bayes estimation of the parameter in a uniform distribution U(0, ) based on randomly right censored data. By mimicking the form of the Bayes estimator, an empirical Bayes estimator [image omitted] is constructed. The asymptotic optimality of [image omitted] is investigated. It is shown that under certain conditions, [image omitted] is asymptotically optimal with a rate of convergence n-r/2(r+1), where n is the number of past data available when the present estimation problem is considered, and 0 2, and r is a positive integer related to some conditions.