Empirtical estimates with minimal d-risk for discrete exponential families

Abstract

We develop an empirical d-a posteriori approach to estimations with uniformly minimal d-risk, when the a priori distribution is completely unknown. For a scalar parameter of a discrete exponential family we construct empirical estimates based on archive data and prove the convergence of the empirical d-risk to the true one. As an example we adduce the estimation of the Poisson distribution parameter. We numerically study the accuracy of the estimates by a statistical modeling technique. © 2010 Allerton Press, Inc.