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Edgeworth expansions for two‐stage sampling with applications to stratified and cluster sampling
Author(s) -
Mirakhmedov Sherzod M.,
Jammalamadaka Sreenivasa R.,
Ekström Magnus
Publication year - 2015
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11266
Subject(s) - cluster sampling , stratified sampling , statistics , studentized range , sampling (signal processing) , sampling design , multistage sampling , mathematics , term (time) , sample (material) , confidence interval , population , cluster (spacecraft) , sample size determination , econometrics , demography , standard error , computer science , sociology , physics , chemistry , filter (signal processing) , chromatography , quantum mechanics , computer vision , programming language
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 © 2015 The Authors. The Canadian Journal of Statistics published by Wiley Periodicals, Inc. on behalf of Statistical Society of Canada