A Unifying Parametric Framework for Estimating Finite Population Totals from Complex Samples

Abstract

We propose a unifying framework for improving the efficiency of design-based estimators of finite population characteristics in the presence of full response. We call the framework a Parametric (PA) approach. The PA framework, an extension of the model-assisted theory, uses an algorithmic approach driven by the observed data. The algorithm identifies the relevant subset of auxiliary variables related to the outcome, and the known population totals of these variables are used to compute the PA estimator. We apply the PA framework to three important estimation problems: the identification of the functional form of a design-based estimator based on the observed data; the identification working or assisting model; and the development of the methodology for creating new design-based estimators. The PA estimators are theoretically justified and evaluated by simulations. This dissertation is limited to single-stage sample designs with full response, but the framework can be extended to other sample designs and for estimation with nonresponse.