We propose to estimate non-linear small area population quantities by using Empirical
Best (EB) estimators based on a nested error model. EB estimators are obtained by
Monte Carlo approximation. We focus on poverty indicators as particular non-linear
quantities of interest, but the proposed methodology is applicable to general non-linear
quantities. Small sample properties of EB estimators are analyzed by model-based and
design-based simulation studies. Results show large reductions in mean squared error
relative to direct estimators and estimators obtained by simulated censuses. An
application is also given to estimate poverty incidences and poverty gaps in Spanish
provinces by sex with mean squared errors estimated by parametric bootstrap. In the
Spanish data, results show a significant reduction in coefficient of variation of the
proposed EB estimators over direct estimators for most domains
