Spatial modelling in small area estimation via the cross-entropy method

Estimation of population characteristics for sub-national domains or smaller regions can be considered one of the important issues of statistical surveys. In particular, geographically defined domains such as regions, states, districts and local government areas may be of interest. One of general methods 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 either the area or the individual random effects (defined, for example, by a contiguity criterion) are correlated, with the correlation decaying to zero as the distance between these areas increases. In this talk, we consider the Cross-Entropy method to spatial modelling in small area estimation using Monte Carlo simulation to find a contiguity matrix that maximizes some measure of spatial association between areas/units. 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.