The Estimation of the Mean Squared Error of Small-Area Estimators

Small-area estimation has received considerable attention in recent years because of a growing demand for reliable small-area statistics. The direct-survey estimators, based only on the data from a given small area (or small domain), are likely to yield unacceptably large standard errors because of small sample size in the domain. Therefore, alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the efficiency. These estimators use models, either implicitly or explicitly, that connect the small areas through supplementary (e.g., census and administrative) data. For example, simple synthetic estimators are based on implicit modeling. In this article, three small-area models, of Battese, Harter, and Fuller (1988), Dempster, Rubin, and Tsutakawa (1981), and Fay and Herriot (1979), are investigated. These models are all special cases of a general mixed linear model involving fixed and random effects, and a small-area mean can be expr...