This work deals with empirical Bayes estimation for the reproduction parameter of Borel-Tanner distributions. Losses of two types are considered: squared and linex error losses. For each type of error loss, a nonparametric empirical Bayes estimator is proposed and its associated asymptotic optimality is investigated. It is shown that under a certain condition, the regrets of the proposed empirical Bayes estimators converge to zero at a rate O (n- λ / 2) for some number λ, 0 < λ < 2. An example fulfilling the required condition for convergence is also provided. © 2009 Elsevier B.V. All rights reserved.
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