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Simple design-efficient calibration estimators for rejective and high-entropy sampling

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  • Z. Tan

Abstract

For survey calibration, consider the situation where the population totals of auxiliary variables are known or where auxiliary variables are measured for all population units. For each situation, we develop design-efficient calibration estimators under rejective or high-entropy sampling. A general approach is to extend efficient estimators for missing-data problems with independent and identically distributed data to the survey setting. We show that this approach effectively resolves two long-standing issues in existing approaches: how to achieve design efficiency regardless of a linear superpopulation model in generalized regression and calibration estimation, and how to find a simple approximation in optimal regression estimation. Moreover, the proposed approach sheds light on several issues that seem not to be well studied in the literature. Examples include use of the weighted Kullback--Leibler distance in calibration estimation, and efficient estimation allowing for misspecification of a nonlinear superpopulation model. Copyright 2013, Oxford University Press.

Suggested Citation

  • Z. Tan, 2013. "Simple design-efficient calibration estimators for rejective and high-entropy sampling," Biometrika, Biometrika Trust, vol. 100(2), pages 399-415.
  • Handle: RePEc:oup:biomet:v:100:y:2013:i:2:p:399-415
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    File URL: http://hdl.handle.net/10.1093/biomet/ass090
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    Cited by:

    1. Xiaojun Mao & Zhonglei Wang & Shu Yang, 2023. "Matrix completion under complex survey sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(3), pages 463-492, June.
    2. Changbao Wu & Wilson W. Lu, 2016. "Calibration Weighting Methods for Complex Surveys," International Statistical Review, International Statistical Institute, vol. 84(1), pages 79-98, April.
    3. Zhan Liu & Chaofeng Tu & Yingli Pan, 2022. "Model-assisted calibration with SCAD to estimated control for non-probability samples," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 849-879, October.
    4. Tan, Zhiqiang, 2014. "Second-order asymptotic theory for calibration estimators in sampling and missing-data problems," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 240-253.

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