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Estimating General Parameters from Non-Probability Surveys Using Propensity Score Adjustment

Author

Listed:
  • Luis Castro-Martín

    (Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain)

  • María del Mar Rueda

    (Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain)

  • Ramón Ferri-García

    (Department of Statistics and Operational Research, University of Granada, 18071 Granada, Spain)

Abstract

This study introduces a general framework on inference for a general parameter using nonprobability survey data when a probability sample with auxiliary variables, common to both samples, is available. The proposed framework covers parameters from inequality measures and distribution function estimates but the scope of the paper is broader. We develop a rigorous framework for general parameter estimation by solving survey weighted estimating equations which involve propensity score estimation for units in the non-probability sample. This development includes the expression of the variance estimator, as well as some alternatives which are discussed under the proposed framework. We carried a simulation study using data from a real-world survey, on which the application of the estimation methods showed the effectiveness of the proposed design-based inference on several general parameters.

Suggested Citation

  • Luis Castro-Martín & María del Mar Rueda & Ramón Ferri-García, 2020. "Estimating General Parameters from Non-Probability Surveys Using Propensity Score Adjustment," Mathematics, MDPI, vol. 8(11), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2096-:d:449770
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    References listed on IDEAS

    as
    1. Jack Kuang Tsung Chen & Richard L. Valliant & Michael R. Elliott, 2019. "Calibrating non‐probability surveys to estimated control totals using LASSO, with an application to political polling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(3), pages 657-681, April.
    2. Jelke Bethlehem, 2010. "Selection Bias in Web Surveys," International Statistical Review, International Statistical Institute, vol. 78(2), pages 161-188, August.
    3. Bart Buelens & Joep Burger & Jan A. van den Brakel, 2018. "Comparing Inference Methods for Non‐probability Samples," International Statistical Review, International Statistical Institute, vol. 86(2), pages 322-343, August.
    4. Zhao, Puying & Haziza, David & Wu, Changbao, 2020. "Survey weighted estimating equation inference with nuisance functionals," Journal of Econometrics, Elsevier, vol. 216(2), pages 516-536.
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