The aim of small area estimation (SAE ) is to produce reliable estimates for each small area for the target variables of interest, whenever the direct estimates cannot be considered enough reliable, i.e., the correspondent variances are too high.
SAE estimators borrow strength from neighbouring areas and auxiliary information deriving from administrative data. Another relevant source of information derives from data measured on previous occasions. In this case specific models can be defined in order to take into account the augmented amount of information with respect to cross-sectional data. Furthermore it is possible to exploit potential correlations between data from the same area on different times. In fact, most repeated survey samples usually include only partial replacement of sample units therefore gain in efficiency can be achieved by borrowing strength from other areas and other time occasions.
Two alternative model specifications are described in the literature. The former is based on linear mixed models in which an additional time depending random effect is added both in unit and area level framework, while the latter refers to state space models specifications.
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