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Edgeworth expansions for two‐stage sampling with applications to stratified and cluster sampling
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https://doi.org/10.1002/cjs.11266Abstract
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.
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