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Design-Unbiased Statistical Learning in Survey Sampling

Author

Listed:
  • Luis Sanguiao Sande

    (Instituto Nacional de Estadística)

  • Li-Chun Zhang

    (University of Southampton
    Statistisk Sentralbyraa
    Universitetet i Oslo)

Abstract

Design-consistent model-assisted estimation has become the standard practice in survey sampling. However, design consistency remains to be established for many machine-learning techniques that can potentially be very powerful assisting models. We propose a subsampling Rao-Blackwell method, and develop a statistical learning theory for exactly design-unbiased estimation with the help of linear or non-linear prediction models. Our approach makes use of classic ideas from Statistical Science as well as the rapidly growing field of Machine Learning. Provided rich auxiliary information, it can yield considerable efficiency gains over standard linear model-assisted methods, while ensuring valid estimation for the given target population, which is robust against potential mis-specifications of the assisting model, even if the design consistency of following the standard recipe for plug-in model-assisted estimator cannot be established.

Suggested Citation

  • Luis Sanguiao Sande & Li-Chun Zhang, 2021. "Design-Unbiased Statistical Learning in Survey Sampling," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 714-744, August.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:2:d:10.1007_s13171-020-00224-1
    DOI: 10.1007/s13171-020-00224-1
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    References listed on IDEAS

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    1. Gordon, Louis & Olshen, Richard A., 1980. "Consistent nonparametric regression from recursive partitioning schemes," Journal of Multivariate Analysis, Elsevier, vol. 10(4), pages 611-627, December.
    2. Kelly S. McConville & Daniell Toth, 2019. "Automated selection of post‐strata using a model‐assisted regression tree estimator," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 389-413, June.
    3. Lorenzo Fattorini, 2006. "Applying the Horvitz-Thompson criterion in complex designs: A computer-intensive perspective for estimating inclusion probabilities," Biometrika, Biometrika Trust, vol. 93(2), pages 269-278, June.
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