Conditional Properties of Post‐Stratified Estimators Under Normal Theory

Robert J. Casady and Richard Valliant


Post-stratification is a common technique for improving precision of estimators by using data items not available at the design stage of a survey. In large, complex samples, the vector of Horvitz-Thompson estimators of survey target variables and of post-stratum population sizes will, under appropriate conditions, be approximately multivariate normal. This large sample normality leads to a new post-stratified regression estimator, which is analogous to the linear regression estimator in simple random sampling. We derive the large sample design bias and mean squared errors of this new estimator, the standard post-stratified estimator, the Horvitz-Thompson estimator, and a ratio estimator. We use both real and artificial populations to study empirically the conditional and unconditional properties of the estimators in multistage sampling.