Linking of sample data to small areas

We consider methods for estimating the means of survey variables in domains of a finite population, where sample sizes are too small to obtain reliable direct estimates. We construct generalized compositions from the direct and traditional design-based synthetic estimators and propose the methodology for evaluating their coefficients. This methodology measures similarities among sample elements and estimates of the domain means. We propose the compositions for two cases of auxiliary information: domain-level characteristics are available; true means of auxiliary variables are available for the estimation domains, and unit-level auxiliary vectors are known for the sample elements. In the simulation study, we show where the generalized compositions improve the traditional synthetic and composite estimators.