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A new approach to weighting and inference in sample surveys

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  • Jean-François Beaumont

Abstract

The validity of design-based inference is not dependent on any model assumption. However, it is well known that estimators derived through design-based theory may be inefficient for the estimation of population totals when the design weights are weakly related to the variables of interest and have widely dispersed values. We propose estimators that have the potential to improve the efficiency of any estimator derived under the design-based theory. Our main focus is limited to the improvement of the Horvitz--Thompson estimator, but we also discuss the extension to calibration estimators. The new estimators are obtained by smoothing design or calibration weights using an appropriate model. Our approach to inference requires the modelling of only one variable, the weight, and it leads to a single set of smoothed weights in multipurpose surveys. This is to be contrasted with other model-based approaches, such as the prediction approach, in which it is necessary to postulate and validate a model for each variable of interest leading potentially to variable-specific sets of weights. Our proposed approach is first justified theoretically and then evaluated through a simulation study. Copyright 2008, Oxford University Press.

Suggested Citation

  • Jean-François Beaumont, 2008. "A new approach to weighting and inference in sample surveys," Biometrika, Biometrika Trust, vol. 95(3), pages 539-553.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:3:p:539-553
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    File URL: http://hdl.handle.net/10.1093/biomet/asn028
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    Citations

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    Cited by:

    1. D. R. Cox, 2009. "Randomization in the Design of Experiments," International Statistical Review, International Statistical Institute, vol. 77(3), pages 415-429, December.
    2. Lingxiao Wang & Barry I. Graubard & Hormuzd A. Katki & and Yan Li, 2020. "Improving external validity of epidemiologic cohort analyses: a kernel weighting approach," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1293-1311, June.
    3. Heng Chen & Rallye Shen, 2017. "The Bank of Canada 2015 Retailer Survey on the Cost of Payment Methods: Calibration for Single-Location Retailers," Technical Reports 109, Bank of Canada.
    4. Ramón Ferri-García & Jean-François Beaumont & Keven Bosa & Joanne Charlebois & Kenneth Chu, 2022. "Weight smoothing for nonprobability surveys," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 619-643, September.
    5. A. Sikov & J. M. Stern, 2019. "Application of the full Bayesian significance test to model selection under informative sampling," Statistical Papers, Springer, vol. 60(1), pages 89-104, February.
    6. 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.
    7. Ray Chambers & Setareh Ranjbar & Nicola Salvati & Barbara Pacini, 2022. "Weighting, informativeness and causal inference, with an application to rainfall enhancement," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 1584-1612, October.
    8. Jeremy Seeman & Yajuan Si & Jerome P. Reiter, 2024. "Differentially Private Population Quantity Estimates via Survey Weight Regularization," NBER Chapters, in: Data Privacy Protection and the Conduct of Applied Research: Methods, Approaches and their Consequences, National Bureau of Economic Research, Inc.
    9. Daniel Bonnéry & F. Jay Breidt & François Coquet, 2017. "Kernel estimation for a superpopulation probability density function under informative selection," METRON, Springer;Sapienza Università di Roma, vol. 75(3), pages 301-318, December.
    10. Danutė Krapavickaitė, 2022. "Impact of Stratum Composition Changes on the Accuracy of the Estimates in a Sample Survey," Mathematics, MDPI, vol. 10(7), pages 1-21, March.
    11. Ivan Faiella, 2010. "The use of survey weights in regression analysis," Temi di discussione (Economic working papers) 739, Bank of Italy, Economic Research and International Relations Area.

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