Design-Consistent versus Model-Dependent Estimation for Small Domains

Abstract

For small domains, we have a choice between design-consistent estimators that make the strongest possible use of auxiliary information and model-dependent design-biased alternatives such as the synthetic estimator. In this article, a design-consistent method is developed that borrows strength in the same way that the design-biased synthetic estimator does. The latter has a design-based mean squared error (MSE) advantage in small samples under the supposition that domains resemble each other. Under deviations from that model, however, and with moderate to large samples, the design-consistent method gives a smaller MSE. It also has the advantage that design-based variance estimators and design-based confidence intervals can be easily obtained. This article emphasizes that the choice of estimation method depends on a complex interaction of factors that include sample size, sampling fraction, domain size, and departures from the model.

Key Words:

• Synthetic estimator
• Generalized regression estimator
• Design consistency
• Regression models