Model-assisted optimal allocation for planned domains using composite estimation

This paper develops allocation methods for stratified sample surveys where small area estimates are a priority. Small areas are domains of interest with sample sizes too small to allow traditional direct estimation to be feasible. Composite estimation may then be used, to balance between using a grand mean estimate and an area-specific estimate for each small area. In this paper, we assume stratified sampling where small areas are strata. Similar to Longford (2006), we seek efficient allocations where the aim is to minimise a linear combination of the mean squared errors of composite small area estimators and of an estimator of the overall mean. Unlike Longford, we define mean-squared error in a model-assisted framework, allowing a more natural interpretation of results using an intra-class correlation parameter. This optimal allocation is only available analytically for a special case, and has the unappealing property that some strata may be allocated no sample. Some alternative allocations, including a power allocation with numerically optimized exponent, are found to perform nearly as well as the optimal allocation, but with better practical properties.