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Calibration Estimation in Survey Sampling

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  • Jae Kwang Kim
  • Mingue Park

Abstract

Calibration estimation, where the sampling weights are adjusted to make certain estimators match known population totals, is commonly used in survey sampling. The generalized regression estimator is an example of a calibration estimator. Given the functional form of the calibration adjustment term, we establish the asymptotic equivalence between the functional‐form calibration estimator and an instrumental variable calibration estimator where the instrumental variable is directly determined from the functional form in the calibration equation. Variance estimation based on linearization is discussed and applied to some recently proposed calibration estimators. The results are extended to the estimator that is a solution to the calibrated estimating equation. Results from a limited simulation study are presented. L'estimation par calage, pour laquelle les poids de sondage sont ajustés de manière à ce que certains estimateurs coïncident avec des totaux connus dans la population, est fréquemment utilisée en échantillonnage. L'estimateur par la régression généralisée est un exemple d'un estimateur de calage. Dans le cas où les facteurs d'ajustement sont exprimés selon une forme fonctionnelle, nous établissons l'équivalence asymptotique entre l'estimateur de calage ave celui avec variable instrumentale, où la variable instrumentale est directement déterminée à partir de la forme fonctionnelle dans l'équation de calage. L'estimation de la variance par linéarisation est traitée et appliquée à certains estimateurs de calage proposés récemment. Les résultats sont généralisés à l'estimateur solution de l'équation estimante calée. Les résultats d'une étude par simulation limitée sont présentés.

Suggested Citation

  • Jae Kwang Kim & Mingue Park, 2010. "Calibration Estimation in Survey Sampling," International Statistical Review, International Statistical Institute, vol. 78(1), pages 21-39, April.
    • Handle: RePEc:bla:istatr:v:78:y:2010:i:1:p:21-39
    DOI: 10.1111/j.1751-5823.2010.00099.x
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    References listed on IDEAS

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    1. Montanari, Giorgio E. & Ranalli, M. Giovanna, 2005. "Nonparametric Model Calibration Estimation in Survey Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1429-1442, December.
    2. Yves Tillé, 1998. "Estimation in Surveys Using Conditional Inclusion Probabilities: Simple Random Sampling," International Statistical Review, International Statistical Institute, vol. 66(3), pages 303-322, December.
    3. 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.
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    Cited by:

    1. Hamori, Shigeyuki & Motegi, Kaiji & Zhang, Zheng, 2019. "Calibration estimation of semiparametric copula models with data missing at random," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 85-109.
    2. Kwun Chuen Gary Chan & Sheung Chi Phillip Yam & Zheng Zhang, 2016. "Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 673-700, June.
    3. 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.
    4. 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.
    5. Maria del Mar Rueda, 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 1077-1081, December.
    6. Carol Liu, 2024. "BayesSRW: Bayesian Sampling and Re-weighting approach for variance reduction," Papers 2408.15454, arXiv.org.
    7. Jae Kwang Kim & Zhonglei Wang & Zhengyuan Zhu & Nathan B. Cruze, 2018. "Combining Survey and Non-survey Data for Improved Sub-area Prediction Using a Multi-level Model," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(2), pages 175-189, June.
    8. Gelein, Brigitte & Haziza, David & Causeur, David, 2014. "Preserving relationships between variables with MIVQUE based imputation for missing survey data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 197-208.
    9. Jae‐Kwang Kim & Siu‐Ming Tam, 2021. "Data Integration by Combining Big Data and Survey Sample Data for Finite Population Inference," International Statistical Review, International Statistical Institute, vol. 89(2), pages 382-401, August.
    10. West Brady T. & Sakshaug Joseph W. & Aurelien Guy Alain S., 2018. "Accounting for Complex Sampling in Survey Estimation: A Review of Current Software Tools," Journal of Official Statistics, Sciendo, vol. 34(3), pages 721-752, September.
    11. 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.

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