Generalized regression estimation for a two-phase sample of tax records

A generalized regression estimator for domains and an approximate estimator of its variance are derived under two-phase sampling for stratification with Poisson selection at each phase. The derivations represent an application of the general framework for regression estimation for two-phase sampling developed by Särndal and Swensson (1987) and Särndal, Swensson and Wretman (1992). The empirical efficiency of the generalized regression estimator is examined using data from Statistics Canada’s annual two-phase sample of tax records. Three particular cases of the generalized regression estimator - two regression estimators and a poststratified estimator - are compared to the Horvitz-Thompson estimator.