Sample size calculation for small-area estimation

We describe a general approach to setting the sampling design in surveys that are planned for making inferences about small areas (sub-domains). The approach requires a specification of the inferential priorities for the areas. Sample size allocation schemes are derived first for the direct estimator and then for composite and empirical Bayes estimators. The methods are illustrated on an example of planning a survey of the population of Switzerland and estimating the mean or proportion of a variable for each of its 26 cantons.