  In this study, simultaneous predictive distributions for independent Poisson
observables were considered and the performance of predictive distributions was
evaluated using the Kullback-Leibler (K-L) loss. This study proposes a class of
empirical Bayesian predictive distributions that dominate the Bayesian
predictive distribution based on the Jeffreys prior. The K-L risk of the
empirical Bayesian predictive distributions is demonstrated to be less than
1.04 times the minimax lower bound.
