The Role of Models in Model-Assisted and Model-Dependent Estimation for Domains and Small Areas

Risto Lehtonen, University of Helsinki
Mikko Myrskylä, University of Pennsylvania
Carl-Eric Särndal, Université de Montréal
Ari Veijanen, Statistics Finland

This paper investigates domain total estimation for model-assisted generalized regression (GREG) and model-dependent EBLUP estimators under probability proportional to size (PPS) sampling. Two particular issues are addressed: (i) how to account for the domain differences in the model formulation, and (ii) how to account for the PPS design. Results are based on Monte Carlo experiments. In the experiments, the bias of GREG estimator remained negligible for all models, and accuracy improved when the PPS size variable was included in the model. For EBLUP, bias was large for weak models, but the bias decreased substantially when the PPS size variable was included in the model. Thus double-use of the auxiliary information seemed profitable. As an alternative to the classic unweighted EBLUP, we propose a new weighted EBLUP estimator for PPS designs. In the experiments the weighted EBLUP behaved much better than the unweighted EBLUP.