On standard errors of model-based small-area estimators

We derive an estimator of the mean squared error (MSE) of the empirical Bayes and composite estimator of the local-area mean in the standard small-area setting. The MSE estimator is a composition of the established estimator based on the conditional expectation of the random deviation associated with the area and a naïve estimator of the design-based MSE. Its performance is assessed by simulations. Variants of this MSE estimator are explored and some extensions outlined.