Survey (CPS), the SIE generally achieved this target reliability, which was considerably better than what the CPS offered, particularly in small states. Even when reliability targets were negotiated in advance, however, the impact of sampling error on the face validity of the estimates was more pronounced than survey designers anticipated. Although the SIE met the target reliability requirements, the state of Alabama protested the large decrease in its poverty rate since the preceding census. The use of small-area models to correct data problems of this type was not yet an established practice at the time.
In some situations, model-based small-area estimation represents a necessary alternative to direct estimation. Some of the earliest examples of small-area estimation include postcensal population estimates from the Census Bureau and economic series produced by researchers at the Bureau of Economic Analysis, even though these precedents use slightly different paradigms.
Several of the basic model-based approaches to small-area estimation emerged decades ago, including:
These basic approaches were followed by a number of refinements, such as mean square estimation and hierarchical Bayes approaches, he noted. Even as these model-based approaches expanded, researchers pointed out that model-assisted estimators could represent a viable alternative in some situations (Särndal and Hidiroglou, 1989; Rao, 2003).
Fay mentioned some reviews of early applications: Small Area Statistics: An International Symposium (Platek et al., 1987) and Indirect Estimators in U.S. Federal Programs (Schaible, 1996), which was based on a 1993 Federal Committee on Statistical Methodology report and includes examples of practice from several agencies. A basic resource on theory for scholars starting out in this area is the classic Small Area Estimation (Rao, 2003). Another useful review of theory is Small Area Estimation: An Appraisal (Ghosh and Rao, 1994).
It is clear that even though the theory of model-based small-area estimation has been available for decades and a number of researchers have expanded the theory, the number of applications is not yet large. Possible reasons are that model-based estimates are more difficult to produce, replicate, and combine with other estimates than direct estimates. Model-based estimates are also more difficult to document and explain to data users. For example, even when estimates of error are produced for an annual series of small-area estimates, users are typically unable to answer other questions from the published information,