Small area estimation of general parameters under complex sampling designs.

When the probabilities of selecting individuals (units) for the sample depend on the outcome values, the selection mechanism is said to be informative. Under informative selection, individuals with certain outcome values appear more often in the sample and, as a consequence, usual inference based on the actual sample without appropriate weighting might be strongly biased. An extension of the empirical best (EB) method for estimation of general non-linear parameters in small areas that handles informative selection by incorporating the sampling weights is proposed. Properties of this new method under complex sampling designs, including informative selection, are analyzed. Results confirm that the proposed weighted estimators significantly reduce the bias of unweighted EB estimators under informative sampling, and compare favorably under non-informative sampling. The proposed method is illustrated through an application to poverty mapping in a State from Mexico.