Abstract

This paper describes an empirical Bayesian estimator of multiple Poisson means based on a novel concept. The idea is to assume two different priors; Jeffreys’ prior for determining the hyperparameter and the uniform prior for the canonical parameter for estimating multiple Poisson means. The validity of this idea is discussed in detail. Furthermore, the empirical Bayesian estimator is constructed using the posterior mean of the canonical parameters instead of that of the mean parameters. The proposed estimator is evaluated using three familiar losses, and the results are found to be very promising. Finally, an actual dataset is analyzed to demonstrate the practical use of the proposed estimator.

摘要

本文描述了基于一个新概念的多重泊松均值的经验贝叶斯估计。这个想法是假设两个不同的先验；用于确定超参数的 Jeffreys 先验和用于估计多个泊松均值的规范参数的统一先验。详细讨论了这个想法的有效性。此外，经验贝叶斯估计量是使用规范参数的后验均值而不是均值参数构建的。所提出的估计器使用三个熟悉的损失进行评估，结果被发现非常有希望。最后，对实际数据集进行了分析，以证明所提出的估计器的实际用途。