A Comparison of Adjusted Bayes Estimators of use in Small Area Estimation

Empirical and Hierarchical Bayes methods are often used to improve the precision design-based estimators in Small Area estimation problems. By the way, when posterior means are used to estimate an ’ensemble’ of parameters, a poor estimate of the empirical distribution function of the ensemble typically results. Several adjusted estimators have been proposed in the literature in order to obtain better estimates of nonlinear function of an ensemble of parameters. In this paper we discuss a set of adjusted estimators with reference to the univariate and multivariate Fay-Herriot models within the framework of Hierarchical Bayesian modeling. The repeated sampling properties of the considered estimators and the associated measures of uncertainty are evaluated by means of a simulation exercise.