Estimating Strata Means in Double Sampling with Corrections Based on Second-Phase Sampling

An estimator for strata means is presented for double sampling for stratification where the first-phase strata estimates are corrected by second-phase subsampling. A variance estimator is derived for the estimated strata weights and for the adjusted strata means. These are compared with two bootstrap variance estimators in a simulation study. The stratum mean estimator has negligible bias, and either bootstrap variance estimator is clearly better than the classical estimator in estimating the true variance. The variability of the strata weights is most reliably estimated by the classical variance estimator.