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Efficient unequal probability resampling from finite populations

Author

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  • Conti, Pier Luigi
  • Mecatti, Fulvia
  • Nicolussi, Federica

Abstract

A resampling technique for probability-proportional-to size sampling designs is proposed. It is essentially based on a special form of variable probability, without replacement sampling applied directly to the sample data, yet according to the pseudo-population approach. From a theoretical point of view, it is asymptotically correct: as both the sample size and the population size increase, under mild regularity conditions the proposed resampling design tends to coincide with the original sampling design under which sample data were collected. From a computational point of view, the proposed methodology is easy to be implemented and efficient, because it neither requires the actual construction of the pseudo-population nor any form of randomization to ensure integer weights and sizes. Empirical evidence based on a simulation study1 indicates that the proposed resampling technique outperforms its two main competitors for confidence interval construction of various population parameters including quantiles.

Suggested Citation

  • Conti, Pier Luigi & Mecatti, Fulvia & Nicolussi, Federica, 2022. "Efficient unequal probability resampling from finite populations," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:csdana:v:167:y:2022:i:c:s0167947321002000
    DOI: 10.1016/j.csda.2021.107366
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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. Lennart Bondesson & Imbi Traat & Anders Lundqvist, 2006. "Pareto Sampling versus Sampford and Conditional Poisson Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 699-720, December.
    3. 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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    Cited by:

    1. Yabu, Takuya, 2023. "On Discrete Probability Distributions to Grasp the Number of Samples in a Population," OSF Preprints yv24f, Center for Open Science.
    2. 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.
    3. 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.

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