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Optimal calibration estimators in survey sampling

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  • Changbao Wu

Abstract

We show that the model-calibration estimator for the finite population mean, which was proposed by Wu & Sitter (2001) through an intuitive argument, is optimal among a class of calibration estimators. We also present optimal calibration estimators for the finite population distribution function, the population variance, the variance of a linear estimator and other quadratic finite population functions under a unified framework. The proposed calibration estimators are optimal under the true model but remain design consistent even if the working model is misspecified. A limited simulation study shows that the improvement of these optimal estimators over the conventional ones can be substantial. The question of when and how auxiliary information can be used for both the estimation of the population mean using a generalised regression estimator and the estimation of its variance through calibration is addressed clearly under the proposed general methodology. Some fundamental issues in using auxiliary information from survey data are also addressed in the context of optimal estimation. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Changbao Wu, 2003. "Optimal calibration estimators in survey sampling," Biometrika, Biometrika Trust, vol. 90(4), pages 937-951, December.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:4:p:937-951
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    Citations

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    Cited by:

    1. Wang, Qihua & Lai, Peng, 2011. "Empirical likelihood calibration estimation for the median treatment difference in observational studies," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1596-1609, April.
    2. Stearns, Matthew & Singh, Sarjinder, 2008. "On the estimation of the general parameter," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4253-4271, May.
    3. Alkaya Aylin & Ayhan H. Öztaş & Esin Alptekin, 2017. "Sequential Data Weighting Procedures for Combined Ratio Estimators in Complex Sample Surveys," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 247-270, June.
    4. 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.
    5. Jason P. Estes & Bhramar Mukherjee & Jeremy M. G. Taylor, 2018. "Empirical Bayes Estimation and Prediction Using Summary-Level Information From External Big Data Sources Adjusting for Violations of Transportability," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 568-586, December.
    6. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    7. 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.
    8. Aylin Alkaya & H. Öztaş Ayhan & Alptekin Esin, 2017. "Sequential Data Weighting Procedures For Combined Ratio Estimators In Complex Sample Surveys," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 247-270, June.
    9. Vahe Avagyan & Stijn Vansteelandt, 2021. "Stable inverse probability weighting estimation for longitudinal studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1046-1067, September.
    10. Barranco-Chamorro, I. & Jiménez-Gamero, M.D. & Moreno-Rebollo, J.L. & Muñoz-Pichardo, J.M., 2012. "Case-deletion type diagnostics for calibration estimators in survey sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2219-2236.
    11. M. Rueda & J.F. Muñoz, 2009. "New Model‐assisted Estimators for the Distribution Function Using the Pseudo Empirical Likelihood Method," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(2), pages 227-244, May.
    12. 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.
    13. María del Mar Rueda & Sergio Martínez-Puertas & Luis Castro-Martín, 2022. "Methods to Counter Self-Selection Bias in Estimations of the Distribution Function and Quantiles," Mathematics, MDPI, vol. 10(24), pages 1-19, December.
    14. Changbao Wu & Shixiao Zhang, 2019. "Comments on: Deville and Särndal’s calibration: revisiting a 25 years old successful optimization problem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1082-1086, December.
    15. Xiaogang Duan & Guosheng Yin, 2017. "Ensemble Approaches to Estimating the Population Mean with Missing Response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 899-917, December.

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