Simultaneous Estimation of the Means of Independent Poisson Laws

Abstract A procedure is derived for simultaneously estimating the means of Poisson populations using independent samples. The total loss is the sum of component, standardized squared error losses. The derived procedure is minimax, generalized Bayes, admissible relative to a large class, and better than using the sample means as estimators of the corresponding population means. The latter procedure is compared with the derived procedure, both numerically and asymptotically.