Hybrid calibration methods for small domain estimation
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Hybrid calibration refers to an approach where techniques of classical calibration and more recent model-assisted calibration are combined for a joint calibration methodology. The classical calibration does not assume a model but uses the original auxiliary data as aggregates, whereas in model calibration, unit-level predictions from a model are used as pseudo auxiliary information. By combining these approaches we introduce hybrid methods, where aggregate data from different levels of the population are supplied to the model-free component and unit-level data are incorporated into the model-assisted component. The choice of the model depends on the type of the target variable. We use here linear and logistic mixed models. In the estimation for population subgroups or domains, the classical calibration fails when domain sample sizes become small. Our hybrid calibration methods were more accurate in small domains. In our studies, the basic model-assisted calibration was usually the best in accuracy, but the method requires population-level information on auxiliary variables in the model. The basic hybrid calibration method overcomes this restriction by including a model-free calibration component in the model-assisted calibration procedure. A new two-level hybrid calibration technique provides a further extension applicable for hierarchically structured populations. In this method, calibration in the model-free part is performed at a higher regional level, instead of the domain level. In our simulation experiments, the two-level hybrid calibration performed well: its accuracy and design bias were comparable to model calibration. The most stable weight distributions were obtained by the two-level method and Ha´jek type estimators developed in the paper.
keywordsAuxiliary Information, Model-assisted Calibration, Mixed Models, Survey Weights, Design- based Simulation Experiments.Authors biographyDepartment of Statistics - University of Helsinki (e-mail: risto.lehtonen@helsinki.fi; ari.veijanen@gmail.com). |
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