On robust small area estimation using a simple random effects model

Robust small area estimation is studied under a simple random effects model consisting of a basic (or fixed effects) model and a linking model that treats the fixed effects as realizations of a random variable. Under this model a model-assisted estimator of a small area mean is obtained. This estimator depends on the survey weights and remains design-consistent. A model-based estimator of its mean squared error (MSE) is also obtained. Simulation results suggest that the proposed estimator and Kott's (1989) model-assisted estimator are equally efficient, and that the proposed MSE estimator is often much more stable than Kott's MSE estimator, even under moderate deviations of the linking model. The method is also extended to nested error regression models.