On standard errors of model-based small-area estimators
We derive an estimator of the mean squared error (MSE)
of the empirical Bayes cnd composite estimator of the
local-area mean in the standard small-asea 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 naive estimator of the design-based MSE.
Its performance is assessed by simulations.
Variants of this MSE estimator are explored and some extensions outlined.
Survey Methodology 33, 69-79, 2007.