Optimal sample allocation conditioned on a small area model, estimator, and auxiliary data

Abstract

We have studied optimal sample allocation, associated with small area estimation, when the objective is to obtain as accurate estimates as possible, for the population and for the subpopulations, called as areas here. It is a question of a two-level optimization problem. The basic premise is composed of planned areas, stratified sampling, and small overall sample size predetermined by restricted time and budget resources. Low sample sizes are common in market surveys. During this thesis, we have developed new allocation methods, based on a small area model, estimator, and auxiliary data. The final method, the three-term Pareto allocation, is based on the three terms of the mean-squared error estimator for the area total empirical best linear unbiased predictor estimator, and on the Pareto optimization technique. The performance of the final method has improved, compared with our other model-based allocations. We compare the performances of our allocations with the reference allocations, selected from the literature, through design-based sample simulations using real data. The selection criterion is the diversity in optimality associated with the allocations. From the point of view of the performance, the most competing allocations are the nonlinear programming and the Costa allocations. Model-based estimation produces more accurate estimates than design-based estimation under the research population structure. Our allocation leads to estimates with the best accuracies and moderately small biases. The results support the conditioning of the sample allocation on the model and on the estimator. It is also important to consider the balance between the area level and the population level estimation, and between the accuracy and the bias of the estimates.