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A Bootstrap Variance Procedure for the Generalised Regression Estimator

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  • Marius Stefan
  • Michael A. Hidiroglou

Abstract

The generalised regression estimator (GREG) uses auxiliary data that are available from the finite population to improve the efficiency of the estimator of a total (mean). Estimators of the variance of GREG that have been proposed in the sampling literature include those based on Taylor linearisation and the jackknife techniques. Approximations based on Taylor expansions are reasonable for large samples. However, when the sample size is small, the Taylor‐based variance estimator has a large negative bias. The jackknife variance estimators overestimate the variance of GREG for small sample sizes. We offset these setbacks using a bootstrap procedure for estimating the variance of the GREG. The method uses a bootstrap population constructed with the model underlying the GREG estimator. Repeated samples are selected in the bootstrap population according to the design used to select the initial sample, and the variability associated with these bootstrap samples is used to compute the proposed bootstrap variance estimator. Simulations show that the new bootstrap estimator has a small bias for samples that have few observations.

Suggested Citation

  • Marius Stefan & Michael A. Hidiroglou, 2023. "A Bootstrap Variance Procedure for the Generalised Regression Estimator," International Statistical Review, International Statistical Institute, vol. 91(2), pages 294-317, August.
    • Handle: RePEc:bla:istatr:v:91:y:2023:i:2:p:294-317
    DOI: 10.1111/insr.12528
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
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