Development and evaluation of an optimal composite estimator in spatial microsimulation small area estimation

A range of data are of geographic interest but are not available at small area level from existing data sources. Small area estimation (SAE) offers techniques to estimate population parameters of target variables to detailed scales based on relationships between those target variables and relevant auxiliary variables. The resulting indirect small area estimate can deliver a lower mean squared error compared to its direct survey estimate given that variance can be reduced markedly even if bias increases. Spatial microsimulation SAE approaches are widely utilised but only beginning to engage with the potential of composite estimators that use a weighted combination of indirect and direct estimators to reduce further the mean squared error of the small area estimate compared to an indirect SAE estimator alone. This paper advances these approaches by constructing for the first time in the microsimulation literature an optimal composite estimator for such SAE approaches in which the combining weight is calculated from the mean squared errors of the two estimators, thus optimising the reduction in MSE of the resulting small area estimates. This optimal composite estimator is demonstrated and evaluated in a model-based simulation study and application based on real data.