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Some design properties of a rejective sampling procedure

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  • Wayne A. Fuller

Abstract

Occasionally, a selected probability sample may appear undesirable with respect to the available auxiliary information. In such a situation, the practitioner might consider rejecting the sample and selecting a new set of sample elements. We consider a procedure in which the probability sample is rejected unless the sample mean of an auxiliary vector is within a specified distance of the population mean. It is proven that the large sample mean and variance of the regression estimator for the rejective sample are the same as those of the regression estimator for the original selection procedure. Likewise, the usual estimator of variance for the regression estimator is appropriate for the rejective sample. In a Monte Carlo experiment, the large sample properties hold for relatively small samples and the Monte Carlo results are in agreement with the theoretical orders of approximation. The efficiency effect of the described rejective sampling is o(n N -super- - 1, where n N is the expected sample size, but the effect can be important for particular samples. For example, rejective sampling can be used to eliminate those samples that give negative weights for the regression estimator. Copyright 2009, Oxford University Press.

Suggested Citation

  • Wayne A. Fuller, 2009. "Some design properties of a rejective sampling procedure," Biometrika, Biometrika Trust, vol. 96(4), pages 933-944.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:4:p:933-944
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    File URL: http://hdl.handle.net/10.1093/biomet/asp042
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    Cited by:

    1. Stefan Marius & Hidiroglou Michael A., 2020. "A Procedure for Estimating the Variance of the Population Mean in Rejective Sampling," Journal of Official Statistics, Sciendo, vol. 36(1), pages 173-196, March.
    2. Zhong, Ping-Shou & Chen, Sixia, 2014. "Jackknife empirical likelihood inference with regression imputation and survey data," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 193-205.
    3. Yves G. Berger, 2020. "An empirical likelihood approach under cluster sampling with missing observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 91-121, February.
    4. R. Benedetti & M. S. Andreano & F. Piersimoni, 2019. "Sample selection when a multivariate set of size measures is available," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 1-25, March.
    5. Cindy L. Yu & Jie Li & Michael G. Karl & Todd J. Krueger, 2020. "Obtaining a Balanced Area Sample for the Bureau of Land Management Rangeland Survey," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(2), pages 250-275, June.
    6. Yves G. Berger, 2023. "Unconditional empirical likelihood approach for analytic use of public survey data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 383-410, March.
    7. Hervé Cardot & Camelia Goga & Pauline Lardin, 2014. "Variance Estimation and Asymptotic Confidence Bands for the Mean Estimator of Sampled Functional Data with High Entropy Unequal Probability Sampling Designs," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 516-534, June.
    8. Y. G. Berger & O. De La Riva Torres, 2016. "Empirical likelihood confidence intervals for complex sampling designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 319-341, March.
    9. Oǧuz-Alper, Melike & Berger, Yves G., 2020. "Modelling multilevel data under complex sampling designs: An empirical likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    10. Yves Tillé, 2022. "Some Solutions Inspired by Survey Sampling Theory to Build Effective Clinical Trials," International Statistical Review, International Statistical Institute, vol. 90(3), pages 481-498, December.
    11. Yves G. Berger & Ewa Kabzińska, 2020. "Empirical Likelihood Approach for Aligning Information from Multiple Surveys," International Statistical Review, International Statistical Institute, vol. 88(1), pages 54-74, April.

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