Dispersion Parameter of Poisson-Gamma Model in the Small Area Estimation

The Poisson-gamma model is useful as a population model for estimating the means of small areas. We consider the Empirical Bayes estimator and the confidence interval for small area mean. When sample sizes are small we frequently encounter the inaccuracy in estimating the dispersion parameters provided the inverse dispersion parameter is small. We investigate the statistical properties of mean squared error and the confidence interval in terms of coverage probability through a Monte Carlo simulation study. In this paper we are restricted to the gamma prior with fixed parameters but it would be more reasonable to assume hierachical prior distributions for the parameters. Furthermore we may consider a Poisson loglinear model for the Poisson mean θ d if auxiliary information of covariates is available.