Pfeffermann and Sverchkov (2007) considered Small Area Estimation (SAE) for the case where the selection of the sampled areas is informative in the sense that the area sampling probabilities are related to the true (unknown) area means, and the sampling of units within the selected areas is likewise informative with probabilities that are related to the values of the study variable; in both cases after conditioning on the model covariates. In this paper we extend this approach to the practical situation of incomplete response at the unit level, and where the response is not missing at random (NMAR). The proposed extension consists of identifying the model holding for the observed responses and using that model for estimating the response probabilities by application of the Missing Information Principle. Once the response probabilities are estimated, we apply the approach of Pfeffermann and Sverchkov (2007) to the observed data for the responding units, with the unit sampling probabilities replaced by the products of the sampling probabilities and the estimated response probabilities. A bootstrap procedure for estimating the MSE of the proposed predictors is developed. We illustrate our approach by a small simulation study and by application to a real data set.

Key words:

complement-sample distribution, estimating equations, missing information principle (MIP), population distribution, respondents model, sample distribution.


Pfeffermann, D. and Sverchkov, M. (2007). Small-area estimation under informative probability sampling of areas and within the selected areas. Journal of the American Statistical Association, 102, 1427–1439.