  In this paper, we consider simultaneous estimation of Poisson parameters in
situations where we can use side information in aggregated data. We use
standardized squared error and entropy loss functions. Bayesian shrinkage
estimators are derived based on conjugate priors. We compare the risk functions
of direct estimators and Bayesian estimators with respect to different priors
that are constructed based on different subsets of observations. We obtain
conditions for domination and also prove minimaxity and admissibility in a
simple setting.
