A shrinkage method to the multiplicative model when Poisson random variables are observed in the form of two-way contingency tables (Efficiencies of Estimation Procedures in Various Statistical Models)

Abstract

Shrinkage estimation of Poisson means is considered when observations are given in the form of a two-way contingency table. Assuming a multiplicative Poisson model, introduce the estimators which shrink to the specified values or an order statistic in one dimension and in two dimensions, proposed by Chang and Shinozaki (2022), are considered and are shown to dominate the maximum likelihood estimator (MLE) under normalized squared error loss. Further, Assuming the full model, shrinkage to the multiplicative model is devised to improve upon the unbiased estimator by finding out the patterns where the observed frequency is not smaller than the estimated frequency for each cell.