Local polynomial estimation for a small area mean under informative sampling - ARCHIVED

Model-based methods are required to estimate small area parameters of interest, such as totals and means, when traditional direct estimation methods cannot provide adequate precision. Unit level and area level models are the most commonly used ones in practice. In the case of the unit level model, efficient model-based estimators can be obtained if the sample design is such that the sample and population models coincide: that is, the sampling design is non-informative for the model. If on the other hand, the sampling design is informative for the model, the selection probabilities will be related to the variable of interest, even after conditioning on the available auxiliary data. This will imply that the population model no longer holds for the sample. Pfeffermann and Sverchkov (2007) used the relationships between the population and sample distribution of the study variable to obtain approximately unbiased semi-parametric predictors of the area means under informative sampling schemes. Their procedure is valid for both sampled and non-sampled areas.