On overall sampling plan for small area estimation

Abstract

The time and budget restrictions in survey sampling can impose limits on the area sample sizes. This may reduce the possibility to obtain area-specific and population parameters estimates with adequate precision. Market research companies and institutes for producing official statistics face frequently this problem. Various models and methods for small area estimation (SAE) have been developed to solve this problem. The sample allocation must support the selected model and method to ensure efficient estimation and must be implemented in the design phase of the survey. The proposed allocation is developed by incorporating auxiliary information, a model, and an estimation method. The estimated parameters are area and population totals. The performance of this allocation is assessed through design-based simulation experiments using real, regularly collected register data. Five other allocations selected from the literature serve as references. Model-based estimation is applied to two allocations and design-based Horvitz-Thompson and model-assisted GREG estimation to four model-free allocations. Four allocations are based on past register data. The allocation with uniquely best performance among all alternatives was not found, but the simulation study supports the comprehensive survey plan where the sampling design is conditioned on the available auxiliary information, selected model, and method.