Robust Hierarchical Bayes Small Area Estimation for Nested Error Regression Model

TL;DR

This paper introduces a robust Bayesian hierarchical model for small area estimation that effectively handles outliers, outperforming existing methods in bias, variability, and coverage, with strong frequentist and Bayesian properties.

Contribution

It proposes a novel robust Bayesian nested error regression model using a two-component scale mixture of normals to mitigate outlier effects in small area estimation.

Findings

Robust Bayesian predictors outperform existing methods in simulations.

The proposed method shows superior bias and coverage properties.

It demonstrates strong frequentist and Bayesian performance in real data.

Abstract

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.