Out of Sample Estimation for Small Areas using Area Level Data

Abstract

A Fay-Herriot type model with independent area effects is often assumed when small area estimates based on area level data are required. However, under this approach out of sample areas are limited to synthetic estimates. In this paper we relax the independent area effects assumption, allowing area random effects to be spatially correlated. Empirical best linear unbiased predictors are then developed for areas in sample as well as those that are not in sample, with variance components estimated via maximum likelihood and residual (restricted) maximum likelihood. An expression for the mean cross-product error (MCPE) matrix of the small area estimators is derived, as is an estimator of this matrix. The estimation approach described in the paper is then evaluated by a simulation study, which compares the new method with other methods of small area estimation for this situation