A comparison of variance estimators for poststratification to estimated control totals

Calibration techniques, such as poststratification, use auxiliary information to improve the efficiency of survey estimates. The control totals, to which sample weights are poststratified (or calibrated), are assumed to be population values. Often, however, the controls are estimated from other surveys. Many researchers apply traditional poststratification variance estimators to situations where the control totals are estimated, thus assuming that any additional sampling variance associated with these controls is negligible. The goal of the research presented here is to evaluate variance estimators for stratified, multi-stage designs under estimated-control (EC) poststratification using design-unbiased controls. We compare the theoretical and empirical properties of linearization and jackknife variance estimators for a poststratified estimator of a population total. Illustrations are given of the effects on variances from different levels of precision in the estimated controls. Our research suggests (i) traditional variance estimators can seriously underestimate the theoretical variance, and (ii) two EC poststratification variance estimators can mitigate the negative bias.