On an improved empirical Bayes estimator for positive exponential families

摘要

This paper deals with the empirical Bayes estimation of the parameter θ in positive exponential families having probability density function (pdf) f(x|θ) = u(x)c(θ) exp(-x/θ). A new empirical Bayes estimator φ_n~* is studied. It is proved that under certain regularity conditions, φ_n~* is asymptotically optimal at a rate (ln~2 n)~((λs-2)/2s), where s > 2 and (2/s) < λ ≤ 2(1 - (1/2)). Examples are given to illustrate the performance of φ_n~*. It is shown that φ_n~* is superior to the empirical Bayes estimator φ_n~(SW) of Singh and Wei [Annals of the Institute of Statistical Mathematics, 44 (1992), 435-449] in the sense that φ_n~* possesses a faster rate of convergence under weaker conditions.