Inference From Stratified Samples: Second-Order Analysis of Three Methods for Nonlinear Statistics

Abstract

For stratified samples and nonlinear statistics that can be expressed as functions of estimated totals, second-order asymptotic expansions of the linearization, jackknife, and balanced repeated-replication variance estimators are obtained. Based on these, comparisons are made in terms of their biases. Some higher order asymptotic equivalence results are also established. The special case of a combined ratio estimator is investigated in detail. Some results on bias reduction achieved by the jack-knife and balanced repeated-replication estimators of a nonlinear function of totals are also given.