Empirical E-Bayesian estimation of hierarchical poisson and gamma model using scaled squared error loss function

The hierarchical models have not only a major concern with developing computational schemes but also assist in inferring the multi-parameter problems. The E-Bayesian is the expected Bayesian estimation that can be found by taking the integrals of Bayesian estimator using a hyper-prior with respect to the hyper-parameters. This study introduces the empirical E-Bayesian estimation that is coalesced with hierarchical modeling which prior to this has not been investigated. The scaled squared error loss function (SELF) has been used to estimate the parameter of Hierarchical Poisson-Gamma (HPG) model using empirical E-Bayesian estimation. The empirical E-Posterior risk is considered to be the evaluation standard. In addition, the consistency along with the asymptotic normality of the posterior distribution have been discussed. Furthermore, the empirical Bayes method is used to estimate the values of hyper-parameters via Maximum Likelihood (ML) method. The Monte Carlo simulation is executed to assess the precision of proposed estimators and a real-data application has been analyzed for illustration and comparison purposes.