Robust Hierarchical Bayes Small Area Estimation for the Nested Error Linear Regression Model

Abstract

Standard model-based small area estimates perform poorly in presence of outliers. Sinha & Rao () developed robust frequentist predictors of small area means. In this article, we present a robust Bayesian method to handle outliers in unit-level data by extending the nested error regression model. We consider a finite mixture of normal distributions for the unit-level error to model outliers and produce noninformative Bayes predictors of small area means. Our modelling approach generalises that of Datta & Ghosh () under the normality assumption. Application of our method to a data set which is suspected to contain an outlier confirms this suspicion, correctly identifies the suspected outlier and produces robust predictors and posterior standard deviations of the small area means. Evaluation of several procedures including the M-quantile method of Chambers & Tzavidis () via simulations shows that our proposed method is as good as other procedures in terms of bias, variability and coverage probability of confidence and credible intervals when there are no outliers. In the presence of outliers, while our method and Sinha–Rao method perform similarly, they improve over the other methods. This superior performance of our procedure shows its dual (Bayes and frequentist) dominance, which should make it attractive to all practitioners, Bayesians and frequentists, of small area estimation.