Double-Robust Small Area Estimation

In the context of robust small area estimation (SAE), there are two types of robustness considerations, robustness against model misspecification and robustness against outliers. We propose a method of SAE that has both types of robustness features. The method combines the idea of observed best prediction (OBP), which is known to be more robust against model misspecification than the traditional best linear unbiased prediction (EBLUP) method, and the method of density power divergence (DPD), which is known to be more robust against outliers than the EBLUP. The double robust predictor (DRP) is developed under an area-level model with normal or normal-mixture sampling errors, and under a unit-level model. Another advantage of the DRP method is that it provides an natural estimator of a tuning parameter involved in the DPD. We develop theory about the proposed method, and demonstrate empirical performance of the proposed DRP and its comparison to EBLUP, OBP, a robust version of the EBLUP, and predictors based on the DPD. A second-order unbiased estimator of the mean squared prediction error of the DRP is developed and its performance is evaluated. A real-data example is discussed.