ABSTRACT
A simple random sample (SRS) from the US population is likely to be inefficient because only a small fraction of American households have net worth over a million dollars; most returned surveys in an SRS will contain few members of the population of interest. The challenge is to obtain a sufficiently large probability sample of the rare population for the desired accuracy while controlling costs. This chapter describes survey designs that have been proposed for estimating the prevalence of a rare characteristic or estimating quantities of interest for a rare population. Nonresponse can be an especial hazard in surveys of rare populations. If population members with the rare characteristic are more likely to be nonrespondents than members without the rare characteristic, estimates of prevalence will be biased. Small area estimation methods rely on auxiliary information and models to obtain estimators of population quantities in domains in which the sample size is too small for a direct estimator to be reliable.
