Bayesian estimator of multiple Poisson means assuming two different priors

This paper describes an empirical Bayesian estimator of multiple Poisson means based on a novel concept. The idea is to assume two different priors; Jeffreys’ prior for determining the hyperparameter and the uniform prior for the canonical parameter for estimating multiple Poisson means. The validity of this idea is discussed in detail. Furthermore, the empirical Bayesian estimator is constructed using the posterior mean of the canonical parameters instead of that of the mean parameters. The proposed estimator is evaluated using three familiar losses, and the results are found to be very promising. Finally, an actual dataset is analyzed to demonstrate the practical use of the proposed estimator.