Foundations of Inference in Survey Sampling

Post-Stratification and Calibration-A Synthesis

“…This is particularly convincing in case of the simple poststratified estimator, which serves as the primary example of post-stratified estimation. Difficulties arise, however, when dealing with complex designs, because {iri , i E sh} is not fixed when conditioning on nh alone, and its distribution easily becomes untraceable (Rao, 1985).…”

Second-order variance estimation in poststratified two-stage sampling

“…where g hic = (a hi M hi /m hi ) k∈s hi hikc (y hik − T * c / M * c ) = S hic (y hic − * c ) and g hc = (1/n h ) i∈s h hic , which is easily shown to be the same as Rao's (1985) adjusted estimator (Yung and Rao, 1996).…”

“…In addition, the poststratified estimator has been shown to be a special case of the generalized regression estimator (Yung and Rao, 1996). Williams (1962) and Rao (1985) discussed the linearization or Taylor series variance estimators for the poststratified estimator for general sample designs. By the usual Taylor approximation at (M…”

“…The jackknife estimator is often used in practice. The jackknife linearization variance estimator is obtained through linearization and is identical to Rao's (1985) variance estimator for the poststratified estimator. Valliant (1993) studied the standard linearization variance estimator, BRR, and the jackknife linearization variance estimator to determine their performances for the conditional variance of the poststratified estimator of a finite population total under a super population model.…”

Estimation in Surveys Using Conditional Inclusion Probabilities: Simple Random Sampling

“…The idea of suppressing the conditional bias has been applied to the ratio estimator by Robinson (1987) who computes the conditional bias of the ratio estimator under assumptions of normality and then corrects it by using an estimator of the conditional bias. The computation and estimation of the conditional bias is presented as an estimation principle by Rao (1985) who applies a conditional bias adjustment to the mean estimator, the ratio estimator in simple random safnpling and stratified sampling design and for domain estimation. More recently Rao (1994) has given a general set-up for estimation using auxiliary information and compares the calibration methods to the conditional approach.…”