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A simple bootstrap method for large entropy unequal probability sampling designs

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  • Tillé, Yves

Abstract

We propose a simple bootstrap method for large entropy unequal probability sampling designs for finite populations. The method belongs to the class of bootstrap techniques that generate replication weights directly for the sampled units. It produces integer replication weights and is applicable to both equal and unequal probability designs characterized by high entropy, such as randomized systematic, pivotal, and maximum entropy designs. Our approach relies on the Dirichlet-Multinomial distribution to generate bootstrap samples while ensuring desirable statistical properties. We provide an efficient implementation in R and validate the method through simulations using real-world data. Results show that the proposed bootstrap estimator performs comparably to established variance estimation techniques while offering greater flexibility for non-linear estimators.

Suggested Citation

  • Tillé, Yves, 2025. "A simple bootstrap method for large entropy unequal probability sampling designs," Statistics & Probability Letters, Elsevier, vol. 224(C).
    • Handle: RePEc:eee:stapro:v:224:y:2025:i:c:s0167715225000872
    DOI: 10.1016/j.spl.2025.110442
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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. 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. 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.
    4. Guillaume Chauvet & Yves Tillé, 2006. "A fast algorithm for balanced sampling," Computational Statistics, Springer, vol. 21(1), pages 53-62, March.
    5. Erika Antal & Yves Tillé, 2014. "A new resampling method for sampling designs without replacement: the doubled half bootstrap," Computational Statistics, Springer, vol. 29(5), pages 1345-1363, October.
    6. Jae Kwang Kim & J. N. K. Rao & Zhonglei Wang, 2024. "Hypotheses Testing from Complex Survey Data Using Bootstrap Weights: A Unified Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 1229-1239, April.
    7. Guillaume Chauvet, 2007. "Bootstrap pour un tirage à plusieurs degrés avec échantillonnage à forte entropie à chaque degré," Working Papers 2007-39, Center for Research in Economics and Statistics.
    8. 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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