CONVERGENCE RATES IN EMPIRICAL BAYES PROBLEMS WITH A WEIGHTED SQUARED-ERROR LOSS. THE PARETO DISTRIBUTION CASE

摘要

We study the problem of estimating the scale parameter θ for a Pareto distribution under a weighted squared-error loss through the empirical Bayes approach. An empirical Bayes estimator is proposed and some asymptotic optimality properties are given. Also, under certain conditions, the empirical Bayes estimator proposed is asymptotically optimal with rate of convergence of order n~(-2/3).