Small area estimates of proportions via empirical Bayes techniques

Empirical Bayes techniques are applied to the problem of “small area” estimation of proportions. Such methods have been previously used to advantage in a variety of situations, as described, for example, by Morris (1983). The basic idea here consists of incorporating random effects and nested random effects into models which reflect the complex structure of a multi-stage sample design, as was originally proposed by Dempster and Tomberlin (1980). Estimates of proportions can be obtained, together with associated estimates of uncertainty. These techniques are applied to simulated data in a Monte Carlo study which compares several available techniques for small area estimation.