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Post Stratification and Conditional Variance Estimation

Richard Valliant


Post stratification is a commonly used estimation technique in sample surveys. After selection of a sample, units are cross-classified into post strata for which known census totals of units are available, and estimates of population totals are obtained in each cell. The technique is used as a means of reducing bias due to poor frame coverage and of reducing variance through stratification. Conditionality arguments imply that inferences using a post averaging over all distributions that might have occurred in a random sampling plan. This paper examines the linearization, balanced repeated replication, and other variance estimators in stratified two-stage sampling to determine whether they estimate conditional or unconditional variances. Theoretical work is supported by a simulation study using data from the U.S. Current Population Survey.