Empirical Bayes Estimation for Uniform Distributions with Random Right Censoring

Abstract

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

Keywords:

• Asymptotically optimal
• Empirical Bayes
• Random censoring
• Rate of convergence
• Regret

Mathematics Subject Classification:

• 62C12