Small Area Estimation Under Informative Sampling and Not Missing at Random Non-Response

Abstract

SummaryPfeffermann and Sverchkov considered small area estimation 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. We extend this approach to the practical situation of incomplete response at the unit level, and where the response is not missing at random. The proposed extension consists of first identifying the model holding for the observed responses and using the model for estimating the response probabilities, and then applying the approach of Pfeffermann and Sverchkov to the observed data with the unit sampling probabilities replaced by the products of the sampling probabilities and the estimated response probabilities. A bootstrap procedure for estimating the mean-squared error of the proposed predictors is developed. We illustrate our approach by a simulation study and by application to a real data set. The simulations also illustrate the consequences of not accounting for informative sampling and/or non-response.