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Traditional direct estimation methods are not efficient for domains of asurvey population with small sample sizes. To estimate the domain proportions,we combine the direct estimators and the regression-synthetic estimators basedon domain-level auxiliary information. For the case of small true proportions,we introduce the design-based linear combination that is a robust alternativeto the empirical best linear unbiased predictor (EBLUP) based on theFay--Herriot model. We also consider an adaptive procedure optimizing asample-size-dependent composite estimator, which depends on a single parameterfor all domains. We imitate the Lithuanian Labor Force Survey, where weestimate the proportions of the unemployed and employed in municipalities. Weshow where the considered design-based compositions and estimators of theirmean square errors are competitive for EBLUP and its accuracy estimation.

Design-based composite estimation of small proportions in small domains