A comparison of adjusted Bayes estimators of an ensemble of small area parameters

Empirical and Hierarchical Bayes methods are often used to improve the precision of design-based estimators in small area estimation problems. By the way, when posterior means are used to estimate the elements of an 'ensemble' of parameters (such as the means of a target variable in a collection of small areas), 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 the empirical distribution function and other nonlinear functions of an ensemble of parameters. In this paper we discuss a set of adjusted estimators for the univariate Fay-Herriot model according to Hierarchical Bayesian solutions. The repeated sampling properties of the considered estimators and the associated measures of uncertainty are evaluated by means of a simulation exercise under the assumption of normality. We also explore the properties of the considered adjusted estimators when normality of random effects fails.