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

Abstract

A two-term Edgeworth expansion for the standardized version of the sample total in a two-stage sampling 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. These results are applied in conjunction with the bootstrap to construct more accurate confidence intervals for the unknown population total in such sampling schemes. Résumé: Les auteurs présentent un développement en deux termes d'une série d'Edgeworth pour l'estimateur du total basé sur un planéchantillonnalà deux phases. Ils obtiennent en particulier des développements asymptotiques formels pour la version studentisée du totaléchantillonnal basé sur unéchantillonnage stratifié et sur unéchantillonnage en grappes. Les auteurs utilisent ces résultats et des méthodes de rééchantillonnage afin de construire des intervalles de confiance plus précis pour le total de la population dans le contexte de ces plans d'échantillonnage. La revue canadienne de statistique 43: 578-599; 2015

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