Second order accurate variance estimation in poststratified two-stage sampling

We proposed new variance estimators for the poststratified estimator of the population total in two-stage sampling. The linearization or Taylor series variance estimator and the jackknife linearization variance estimator are popular for the poststratified estimator. The jackknife linearization variance estimator utilizes the ratio, ^Rc, which balances the weights for the poststrata while the linearization or Taylor series estimator does not. The jackknife linearization variance estimator is equivalent to Rao's (1985) adjusted variance estimator. Our proposed estimator makes use of the ratio, ^R c, in a different shape which is naturally derived from the process of expanding to the second-order Taylor series linearization, while the standard linearization variance estimator is only expanded to the first-order. We investigated the properties and performance of the linearization variance estimator, the jackknife linearization estimator, the proposed variance estimator and its modified version analytically and through simulation study. The simulation study was carried out on both artificially generated data and real data. The result showed that the second order accurate variance estimator and its modified version could be very good candidates for the variance estimation of poststratified estimator of population total.