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

Abstract

With “ensemble properties” of small area estimators, we mean their ability to reproduce the Empirical Distribution Function (EDF) characterizing the collection of underlying small area parameters (means, totals). Good “ensemble properties” may be relevant when estimation of non-linear functionals of the EDF of small area parameters (such as their variance) is needed. Small area estimators associated to the popular Fay-Herriot model are considered. “Bayes estimators”, i.e. posterior means, do not enjoy of good ensemble properties. In this paper three different adjusted predictors are compared, by means of a simulation exercise, under the assumption of correctly specified model. As the distributional assumptions on the random effects are difficult to assess, the considered predictors are compared also with respect to their robustness to the presence of failures in the distributional assumptions on the random effects.