Use of auxiliary information for two-phase sampling - ARCHIVED

Two-phase sampling designs offer a variety of possibilities for use of auxiliary information. We begin by reviewing the different forms that auxiliary information may take in two-phase surveys. We then set up the procedure by which this information is transformed into calibrated weights, which we use to construct efficient estimators of a population total. The calibration is done in two steps: (i) at the population level; (ii) at the level of the first-phase sample. We go on to show that the resulting calibration estimators are also derivable via regression fitting in two steps. We examine these estimators for a special case of interest, namely, when auxiliary information is available for population subgroups called calibration groups. Postrata are the simplest example of such groups. Estimation for domains of interest and variance estimation are also discussed. These results are illustrated by applying them to two-phase designs at Statistics Canada. The general theory for using auxiliary information in two-phase sampling is being incorporated into Statistics Canada's Generalized Estimation System.