A Model-Based Approach: Composite Estimators for Small Area Estimation

Kung-Jong Lui and William G. Cumberland

Abstract:
To reduce the mean-squared-error (MSE) of an estimator in small area estimation, the composite estimator, a weighted sum of two component estimators, is often considered. The difficulties of providing a measure of error with respect to the sampling plan for this estimator, and of deriving the optimal weight to minimize MSE, limit its use. We propose a super-population model-based approach to derive explicit optimal weights for the composite estimator under several models related to the synthetic estimator. In addition, the prediction variance of the composite estimator is easily obtained. A simple test to help in deciding how to best apply these results to small area estimation is given.

Keywords:
Composite estimator; optimal weight; super-population.