Second order accurate variance estimation in poststratified two-stage sampling

We proposed new variance estimators for the poststratified estimator of the populationtotal in two-stage sampling. The linearization or Taylor series variance estimatorand the jackknife linearization variance estimator are popular for the poststratified estimator. The jackknife linearization variance estimator utilizes the ratio, ^Rc, whichbalances the weights for the poststrata while the linearization or Taylor series estimatordoes 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 expandingto the second-order Taylor series linearization, while the standard linearization varianceestimator is only expanded to the first-order. We investigated the propertiesand performance of the linearization variance estimator, the jackknife linearizationestimator, the proposed variance estimator and its modified version analytically andthrough simulation study. The simulation study was carried out on both artificiallygenerated data and real data. The result showed that the second order accuratevariance estimator and its modified version could be very good candidates for thevariance estimation of poststratified estimator of population total.