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Deville and Särndal’s calibration: revisiting a 25-years-old successful optimization problem

Author

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  • Denis Devaud

    (Université de Neuchâtel)

  • Yves Tillé

    (Université de Neuchâtel)

Abstract

In 1992, in a famous paper, Deville and Särndal proposed the calibration method in order to adjust samples on known population totals. This paper had a very important impact in the theory and practice of survey statistics. In this paper, we propose a rigorous formalization of the calibration problem viewed as an optimization problem. We examine the main calibration functions and we discuss the question of the existence of solutions. We also propose an alternate way of solving the optimization problem given by the calibration principle. We finally present a set of simulations in order to compare the different methods.

Suggested Citation

  • Denis Devaud & Yves Tillé, 2019. "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 1033-1065, December.
    • Handle: RePEc:spr:testjl:v:28:y:2019:i:4:d:10.1007_s11749-019-00681-3
    DOI: 10.1007/s11749-019-00681-3
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    References listed on IDEAS

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    1. Kott, Phillip S. & Chang, Ted, 2010. "Using Calibration Weighting to Adjust for Nonignorable Unit Nonresponse," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1265-1275.
    2. Wu C. & Sitter R. R, 2001. "A Model-Calibration Approach to Using Complete Auxiliary Information From Survey Data," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 185-193, March.
    3. Jean-Francois Beaumont & Cynthia Bocci, 2008. "Another look at ridge calibration," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 5-20.
    4. J. Chen, 2002. "Using empirical likelihood methods to obtain range restricted weights in regression estimators for surveys," Biometrika, Biometrika Trust, vol. 89(1), pages 230-237, March.
    5. 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.
    6. Éric Lesage & David Haziza & Xavier D’Haultfœuille, 2019. "A Cautionary Tale on Instrumental Calibration for the Treatment of Nonignorable Unit Nonresponse in Surveys," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 906-915, April.
    7. Alessio Guandalini & Yves Tillé, 2017. "Design-based Estimators Calibrated on Estimated Totals from Multiple Surveys," International Statistical Review, International Statistical Institute, vol. 85(2), pages 250-269, August.
    8. Ted Chang & Phillip S. Kott, 2008. "Using calibration weighting to adjust for nonresponse under a plausible model," Biometrika, Biometrika Trust, vol. 95(3), pages 555-571.
    9. Sanjay Chaudhuri & Mark S. Handcock & Michael S. Rendall, 2008. "Generalized linear models incorporating population level information: an empirical‐likelihood‐based approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 311-328, April.
    10. Jae Kwang Kim & Mingue Park, 2010. "Calibration Estimation in Survey Sampling," International Statistical Review, International Statistical Institute, vol. 78(1), pages 21-39, April.
    11. Matei, Alina & Tille, Yves, 2007. "Computational aspects of order [pi]ps sampling schemes," Computational Statistics & Data Analysis, Elsevier, vol. 51(8), pages 3703-3717, May.
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    Cited by:

    1. Jan Pablo Burgard & Joscha Krause & Ralf Münnich, 2020. "A Study of Discontinuity Effects in Regression Inference based on Web-Augmented Mixed Mode Surveys," Research Papers in Economics 2020-03, University of Trier, Department of Economics.
    2. Anne Konrad & Jan Pablo Burgard & Ralf Münnich, 2021. "A Two‐level GREG Estimator for Consistent Estimation in Household Surveys," International Statistical Review, International Statistical Institute, vol. 89(3), pages 635-656, December.
    3. Alessio Guandalini & Claudio Ceccarelli, 2022. "Impact measurement and dimension reduction of auxiliary variables in calibration estimator using the Shapley decomposition," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(4), pages 759-784, October.

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