We consider simultaneous predictive distributions for independent Poisson observables and evaluate the performance of predictive distributions using the Kullback--Leibler (K-L) loss. We propose 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.

翻译：本文考虑独立泊松观测值的联合预测分布，并使用Kullback-Leibler（K-L）损失评估预测分布的性能。我们提出一类经验贝叶斯预测分布，该分布优于基于Jeffreys先验的贝叶斯预测分布。实证表明，该经验贝叶斯预测分布的K-L风险小于极小极大下界的$1.04$倍。