Convergence rates for empirical Bayes estimation of the scale parameter in a Pareto distribution

Abstract

Let f(χ{divides}θ) = αθα χα+1I(θ,∞)(χ) be the pdf of a Pareto distribution with known shape scale parameter α > 0 and unknown scale parameter θ. We study the problem of estimating the scale parameter θ under a squared-error loss through the nonparametric empirical Bayes approach. An empirical Bayes estimator is proposed and the corresponding asymptotic optimality is also investigated. It is shown that under certain weak conditions the proposed empirical Bayes estimator is asymptotically optimal and the associated rate of convergence is of order O(n- 2 3). © 1993.