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Research article - Peer-reviewed, 2015

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

Mirakhmedov, Sherzod M.; Jammalamadaka, Sreenivasa R.; Ekstrom, Magnus


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. The Canadian Journal of Statistics 43: 578-599; 2015 (C) 2015 The Authors. The Canadian Journal of Statistics published by Wiley Periodicals, Inc. on behalf of Statistical Society of Canada


Bootstrap; cluster sampling; confidence interval; Edgeworth expansion; simple random sampling; stratified sampling; two-stage sampling

Published in

Canadian Journal of Statistics
2015, Volume: 43, number: 4, pages: 578-599

    UKÄ Subject classification

    Probability Theory and Statistics

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