Design-based composite estimation rediscovered

TL;DR

This paper introduces a new design-based approach for small area estimation that optimally combines direct and synthetic estimators, improving efficiency over traditional EBLUP methods.

Contribution

It proposes a two-step procedure for optimal linear combination of estimators and develops a mean square error estimator suitable for this approach.

Findings

The new methods outperform EBLUP in simulation studies.

The approach is applicable to area- and unit-level models.

Efficient estimation of the mean square error is achieved.

Abstract

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.