Comparative Study on Estimation of Poisson Parameter in Decision Theoretic Approach

Abstract

It has become imperative in statistical inference to seek beyond the widely practiced squared loss function to accommodate the asymmetric conditions. An attempt in this direction is generally model-specific and the present work has considered inference on count data, as one such model of importance. In particular, the objective is to study the performance of Bayesian estimators for Poisson parameter based on four well established loss functions. The explicit forms are derived and a comprehensive data analyses has been carried out through a simulation study. The study highlights the distinct behaviour of each of the methods to make an appropriate choice based on the small sample behaviour of the data sets.