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A Bootstrap Variance Estimation Method for Multistage Sampling and Two-Phase Sampling When Poisson Sampling Is Used at the Second Phase

Author

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  • Jean-François Beaumont

    (Statistics Canada, Ottawa, ON K1A 0T6, Canada)

  • Nelson Émond

    (Statistics Canada, Ottawa, ON K1A 0T6, Canada)

Abstract

The bootstrap method is often used for variance estimation in sample surveys with a stratified multistage sampling design. It is typically implemented by producing a set of bootstrap weights that is made available to users and that accounts for the complexity of the sampling design. The Rao–Wu–Yue method is often used to produce the required bootstrap weights. It is valid under stratified with-replacement sampling at the first stage or fixed-size without-replacement sampling provided the first-stage sampling fractions are negligible. Some surveys use designs that do not satisfy these conditions. We propose a simple and unified bootstrap method that addresses this limitation of the Rao–Wu–Yue bootstrap weights. This method is applicable to any multistage sampling design as long as valid bootstrap weights can be produced for each distinct stage of sampling. Our method is also applicable to two-phase sampling designs provided that Poisson sampling is used at the second phase. We use this design to model survey nonresponse and derive bootstrap weights that account for nonresponse weighting. The properties of our bootstrap method are evaluated in three limited simulation studies.

Suggested Citation

  • Jean-François Beaumont & Nelson Émond, 2022. "A Bootstrap Variance Estimation Method for Multistage Sampling and Two-Phase Sampling When Poisson Sampling Is Used at the Second Phase," Stats, MDPI, vol. 5(2), pages 1-19, March.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:2:p:19-357:d:777014
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    References listed on IDEAS

    as
    1. Pier Luigi Conti & Fulvia Mecatti, 2022. "Resampling under Complex Sampling Designs: Roots, Development and the Way Forward," Stats, MDPI, vol. 5(1), pages 1-12, March.
    2. 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.
    3. Conti, Pier Luigi & Mecatti, Fulvia & Nicolussi, Federica, 2022. "Efficient unequal probability resampling from finite populations," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
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