Design-based composite estimation rediscovered

Small area estimation methods are used in surveys, where sample sizes are too small to get reliable direct estimates of parameters in some population domains. We consider design-based linear combinations of direct and synthetic estimators and propose a two-step procedure to approach the optimal combination. We construct the mean square error estimator suitable for this and any other linear composition that estimates the optimal one. We apply the theory to two design-based compositions analogous to the empirical best linear unbiased predictors (EBLUPs) based on the basic area- and unit-level models. The simulation study shows that the new methods are efficient compared to estimation using EBLUP.