Second-order variance estimation in poststratified two-stage sampling

The linearization or Taylor series variance estimator and jackknife linearization variance estimator are popular for poststratified point estimators. In this note we propose a simple second-order linearization variance estimator for the poststratified estimator of the population total in two-stage sampling, using the second-order Taylor series expansion. We investigate the properties of the proposed variance estimator and its modified version and their empirical performance through some simulation studies in comparison to the standard and jackknife linearization variance estimators. Simulation studies are carried out on both artificially generated data and real data.