Publication: Small area estimation of general parameters under complex sampling designs
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2016-04
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Abstract
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.
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Empirical best estimator, Nested-error model, Poverty mapping, Pseudo empirical best estimator, Unit level models