ABSTRACT
The average over simulated censuses of the resulting area estimates is taken as the area estimate and the variance of the estimates is taken as a measure of variability of the estimate. Another approach, based on the empirical best/Bayes methodology, has been recently introduced by Molina and Rao (2010) under the support of the European project SAMPLE (www.sample-project.eu/). This method is similar in spirit to the ELL method in that it combines survey and census auxiliary data. Nevertheless, it gives the estimator with minimum mean squared error or “best predictor” (more exactly, a Monte Carlo approximation of it). This is done under the assumption that there exists a transformation of the incomes of the individuals, or other welfare variable used to measure poverty, such that the transformed incomes follow the BHF model. Mean squared errors of the EB estimators are approximated by a parametric bootstrap method. EB method provides estimators with notably better efficiency (approximately the “best”) because it uses the precious information provided by the sample more extensively by conditioning on the sample responses. A variation of the EB method, called the fast EB method, has been recently introduced by Ferretti and Molina (2012). This method is computationally much faster and therefore it becomes suitable to estimate computationally complex poverty indicators, such as the fuzzy monetary and fuzzy supplementary indicators, in large populations. We report the results of model-based and design-based simulation studies on the relative performance of EB, ELL and direct area-specific estimators. Our results show that the EB estimators can be considerably more efficient than the ELL and the direct estimators, and that the ELL estimators can be even less efficient than the direct estimators. Results also indicate that a bootstrap mean squared error (MSE) estimator appropriately tracks the true MSE.
