Pfeffermann, Danny and Sverchkov, Michail
Small Area Estimation Under Informative Sampling , Southampton, UK Southampton Statistical Sciences Research Institute 13pp.
(S3RI Methodology Working Papers, M03/22).
This article proposes two approaches for small area estimation under informative sampling. The semi-parametric approach makes no assumptions regarding the relationship between the area selection probabilities and the true area means. The proposed predictors under this approach are approximately unbiased for both the sampled and nonsampled areas but the prediction RMSEs can be large particularly for nonsampled areas. The parametric approach models the relationship between the area selection probabilities and the area means and incorporates this relationship into the model for the study variable. As illustrated by a simulation study, the use of this approach can reduce the RMSEs quite significantly.
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