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.

翻译：本文研究在可利用聚合数据中的辅助信息时，同时估计泊松参数的问题。我们采用标准化平方误差和熵损失函数。基于共轭先验推导了贝叶斯收缩估计量。针对基于不同观测子集构建的不同先验，比较了直接估计量与贝叶斯估计量的风险函数。我们得到了主导条件，并在简单设定下证明了极小极大性和可容许性。