Small area estimation of general parameters under complex sampling designs

When the probabilities of selecting the individuals for the sample depend on the outcome values, we say that the selection mechanism is informative. Under informative selection, individuals with certain outcome values appear more often in the sample and therefore the sample is not representative of the population. As a consequence, usual model-based inference based on the actual sample without appropriate weighting might be strongly biased. For estimation of general non-linear parameters in small areas, we propose a model-based pseudo empirical best (PEB) method that incorporates the sampling weights and reduces considerably the bias of the unweighted empirical best (EB) estimators under informative selection mechanisms. We analyze the properties of this new method in simulation experiments carried out under complex sampling designs, including informative selection. Our results confirm that the proposed weighted PEB estimators perform significantly better than the unweighted EB estimators in terms of bias under informative sampling, and compare favorably under non-informative sampling. In an application to poverty mapping in Spain, we compare the proposed weighted PEB estimators with the unweighted EB analogues.