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A two-stage normal hierarchical model called the Fay--Herriot model and theempirical Bayes estimator are widely used to provide indirect and model-basedestimates of means in small areas. However, the performance of the empiricalBayes estimator might be poor when the assumed normal distribution ismisspecified. In this article, we propose a simple modification by usingdensity power divergence and suggest a new robust empirical Bayes small areaestimator. The mean squared error and estimated mean squared error of theproposed estimator are derived based on the asymptotic properties of the robustestimator of the model parameters. We investigate the numerical performance ofthe proposed method through simulations and an application to survey data.

Robust Empirical Bayes Small Area Estimation with Density Power Divergence