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In this study, simultaneous predictive distributions for independent Poissonobservables were considered and the performance of predictive distributions wasevaluated using the Kullback-Leibler (K-L) loss. This study proposes a class ofempirical Bayesian predictive distributions that dominate the Bayesianpredictive distribution based on the Jeffreys prior. The K-L risk of theempirical Bayesian predictive distributions is demonstrated to be less than1.04 times the minimax lower bound.

Nearly minimax empirical Bayesian prediction of independent Poisson observables