Register data in sample allocations for small-area estimation

Abstract

The inadequate control of sample sizes in surveys using stratified sampling and area estimation may occur when the overall sample size is small or auxiliary information is insufficiently used. Very small sample sizes are possible for some areas. The proposed allocation based on multi-objective optimization uses a small-area model and estimation method, and semi-annually collected empirical data. The assessment of its performance at the area and population levels is based on design-based sample simulations, and five previously developed allocations serve as references. The model-based estimator is more accurate than the design-based Horvitz-Thompson estimator and model-assisted regression estimator. Two tradeoff issues are between accuracy and bias and between the area-and population-level qualities of estimates. If the survey uses model-based estimation, the sampling design should incorporate the underlying model and the estimation method.off between the quality of area estimates and the quality of population estimate; and a second trade-off between accuracy and bias.The results support the sampling strategy, in which not only auxiliary information, but also the model and the estimation method should be fixed early, in the design phase of the survey. The proposed allocation uses all information available before choosing the allocation method, avoiding fixed priorities for the importance of estimation at the area and the population levels. Model-related allocationsIn the model-based estimation, the area parameter and often the population parameter estimates result from the statistical model and from the chosen estimator. The proposed allocation (section 2.2) is based on the model and the estimator introduced in section 2.1 and on auxiliary information. Keto and Pahkinen (2010) have used this model and this estimator to describe the relationships between area and sample sizes, estimation results, and area characteristics. One reference allocation (section 2.3) is based on a different area model and on a composite estimator, and uses auxiliary information. These two allocations are "model-related allocations". Table 1 shows the summary details of these allocations. Model and model-based area total estimatorThe area total estimator of the variable of interest is based on the linear mixed model (Battese, Harter, and Fuller, 1988):