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Bootstrap inference for the finite population mean under complex sampling designs

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  • Zhonglei Wang
  • Liuhua Peng
  • Jae Kwang Kim

Abstract

Bootstrap is a useful computational tool for statistical inference, but it may lead to erroneous analysis under complex survey sampling. In this paper, we propose a unified bootstrap method for stratified multi‐stage cluster sampling, Poisson sampling, simple random sampling without replacement and probability proportional to size sampling with replacement. In the proposed bootstrap method, we first generate bootstrap finite populations, apply the same sampling design to each bootstrap population to get a bootstrap sample, and then apply studentization. The second‐order accuracy of the proposed bootstrap method is established by the Edgeworth expansion. Simulation studies confirm that the proposed bootstrap method outperforms the commonly used Wald‐type method in terms of coverage, especially when the sample size is not large.

Suggested Citation

  • Zhonglei Wang & Liuhua Peng & Jae Kwang Kim, 2022. "Bootstrap inference for the finite population mean under complex sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(4), pages 1150-1174, September.
    • Handle: RePEc:bla:jorssb:v:84:y:2022:i:4:p:1150-1174
    DOI: 10.1111/rssb.12506
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    References listed on IDEAS

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    1. Antal, Erika & Tillé, Yves, 2011. "A Direct Bootstrap Method for Complex Sampling Designs From a Finite Population," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 534-543.
    2. Babu, G. Jogesh & Singh, Kesar, 1985. "Edgeworth expansions for sampling without replacement from finite populations," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 261-278, December.
    3. Jean‐François Beaumont & Zdenek Patak, 2012. "On the Generalized Bootstrap for Sample Surveys with Special Attention to Poisson Sampling," International Statistical Review, International Statistical Institute, vol. 80(1), pages 127-148, April.
    4. S Chen & D Haziza & C Léger & Z Mashreghi, 2019. "Pseudo-population bootstrap methods for imputed survey data," Biometrika, Biometrika Trust, vol. 106(2), pages 369-384.
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    6. Xiaojun Mao & Zhonglei Wang & Shu Yang, 2023. "Matrix completion under complex survey sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(3), pages 463-492, June.

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