  National statistical institutes in many countries are now mandated to produce
reliable statistics for important variables such as population, income,
unemployment, health outcomes, etc. for small areas, defined by geography
and/or demography. Due to small samples from these areas, direct sample-based
estimates are often unreliable. Model-based small area estimation is now
extensively used to generate reliable statistics by "borrowing strength" from
other areas and related variables through suitable models. Outliers adversely
influence 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 model
for unit-level data to mitigate outliers. We consider a two-component scale
mixture of normal distributions for the unit-level error to model outliers and
present a computational approach to produce Bayesian predictors of small area
means under a noninformative prior for model parameters. A real example and
extensive simulations convincingly show robustness of our Bayesian predictors
to outliers. Simulations comparison of these two procedures with Bayesian
predictors by Datta and Ghosh (1991) and M-quantile estimators by Chambers et
al. (2014) shows that our proposed procedure is better than the others in terms
of bias, variability, and coverage probability of prediction intervals, when
there are outliers. The superior frequentist performance of our procedure shows
its dual (Bayes and frequentist) dominance, and makes it attractive to all
practitioners, both Bayesian and frequentist, of small area estimation.
