Small area estimation under a two-level model

Lehtonen and Veijanen (1999) proposed a new model-assisted generalized regression (GREG) estimator of a small area mean under a two-level model. They have shown that the proposed estimator performs better than the customary GREG estimator in terms of average absolute relative bias and average median absolute relative error. We derive the mean squared error (MSE) of the new GREG estimator under the two-level model and compare it to the MSE of the best linear unbiased prediction (BLUP) estimator. We also provide empirical results on the relative efficiency of the estimators. We show that the new GREG estimator exhibits better performance relative to the customary GREG estimator in terms of average MSE and average absolute relative error. We also show that, due to borrowing strength from related small areas, the EBLUP estimator exhibits significantly better performance relative to the customary GREG and the new GREG estimators. We provide simulation results under a model-based set-up as well as under a real finite population.