A hybrid algorithm for spatial small area estimation under models with complex contiguity

Estimation of population characteristics for sub-national geographically defined domains such as regions, states, districts and local government areas can be considered one of the important issues of statistical surveys. A general method in small area estimation (SAE) is the use of linear mixed models with area specific random effects to account for between areas variation beyond that explained by auxiliary variables included in the fixed part of the model. In order to use spatial auxiliary information in SAE, it is reasonable to assume that the area random effects (defined, for example, by a contiguity criterion) are correlated. In this paper, we propose a hybrid algorithm based on the Cross-Entropy method to spatial modelling in SAE using Monte Carlo simulation to find a contiguity matrix that maximizes some measure of spatial association between areas. Estimation of the mean squared error of the resulting small area estimators is discussed. The properties of the estimators are evaluated by applying them to the results of farm surveys that have been conducted by the Australian Bureau of Agricultural and Resource Economics.