Edgeworth expansions for two-stage sampling with applications to stratified and cluster sampling

摘要

A two-term Edgeworth expansion for the standardized version of the sample total in a two-stagesampling design is derived. In particular, for the commonly used stratified and cluster sampling schemes,formal two-term asymptotic expansions are obtained for the Studentized versions of the sample total. Theseresults are applied in conjunction with the bootstrap to construct more accurate confidence intervals for theunknown population total in such sampling schemes.