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National statistical institutes in many countries are now mandated to producereliable statistics for important variables such as population, income,unemployment, health outcomes, etc. for small areas, defined by geographyand/or demography. Due to small samples from these areas, direct sample-basedestimates are often unreliable. Model-based small area estimation is nowextensively used to generate reliable statistics by "borrowing strength" fromother areas and related variables through suitable models. Outliers adverselyinfluence standard model-based small area estimates. To deal with outliers,Sinha and Rao (2009) proposed a robust frequentist approach. In this article,we present a robust Bayesian alternative to the nested error regression modelfor unit-level data to mitigate outliers. We consider a two-component scalemixture of normal distributions for the unit-level error to model outliers andpresent a computational approach to produce Bayesian predictors of small areameans under a noninformative prior for model parameters. A real example andextensive simulations convincingly show robustness of our Bayesian predictorsto outliers. Simulations comparison of these two procedures with Bayesianpredictors by Datta and Ghosh (1991) and M-quantile estimators by Chambers etal. (2014) shows that our proposed procedure is better than the others in termsof bias, variability, and coverage probability of prediction intervals, whenthere are outliers. The superior frequentist performance of our procedure showsits dual (Bayes and frequentist) dominance, and makes it attractive to allpractitioners, both Bayesian and frequentist, of small area estimation.

Robust Hierarchical Bayes Small Area Estimation for Nested Error Regression Model