Robust Empirical Bayes Small Area Estimation with Density Power Divergence

Empirical Bayes estimators are widely used to provide indirect and model-based estimates of means in small areas. The most common model is a two-stage normal hierarchical model called Fay-Herriot model. However, due to the normality assumption, it might be highly influenced by the presence of outliers. In this talk, we propose a simple modification of the conventional method by using density power divergence (Basu et al., 1998). The resulting robust marginal likelihood function based on density power divergence is characterized by a scalar parameter controlling the robustness and the proposed likelihood includes the usual marginal likelihood function as a special case. The Bayes estimator based on the likelihood is tail-robust in the sense that the Bayes estimator performs similarly to the direct estimator in outlying areas whereas the usual Bayes estimator does not have such a property. We also show that the estimator of model parameters based on the proposed likelihood is asymptotically normal, and we derive a second order unbiased estimator of the area-specific mean squared error of the robust empirical Bayes estimator. Through simulation studies, we compare the proposed method with some existing methods. Finally, the proposed method is successfully applied to a real data set.