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A unified framework of multiply robust estimation approaches for handling incomplete data

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  • Chen, Sixia
  • Haziza, David

Abstract

Missing data occur frequently in practice. Inverse probability weighting and imputation are regarded as two important approaches for handling missing data. However, the validity of these approaches depends on underlying model assumptions. A new general framework for multiply robust estimation procedures by combining multiple nonresponse and imputation models is proposed in the paper. The proposed method can be used to estimate both smooth and non-smooth parameters defined as the solution of some estimating equations. It includes population means, quantiles, and distribution functions as special cases. The asymptotic results of the proposed methods are established. The results of a simulation study and a real data application suggest that the proposed methods perform well in terms of bias and efficiency.

Suggested Citation

  • Chen, Sixia & Haziza, David, 2023. "A unified framework of multiply robust estimation approaches for handling incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:csdana:v:179:y:2023:i:c:s0167947322002262
    DOI: 10.1016/j.csda.2022.107646
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    References listed on IDEAS

    as
    1. Jae Kwang Kim, 2004. "Fractional hot deck imputation," Biometrika, Biometrika Trust, vol. 91(3), pages 559-578, September.
    2. Sixia Chen & David Haziza, 2017. "Multiply robust imputation procedures for zero-inflated distributions in surveys," METRON, Springer;Sapienza Università di Roma, vol. 75(3), pages 333-343, December.
    3. Peisong Han & Linglong Kong & Jiwei Zhao & Xingcai Zhou, 2019. "A general framework for quantile estimation with incomplete data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(2), pages 305-333, April.
    4. Peisong Han & Lu Wang, 2013. "Estimation with missing data: beyond double robustness," Biometrika, Biometrika Trust, vol. 100(2), pages 417-430.
    5. Peisong Han, 2016. "Intrinsic efficiency and multiple robustness in longitudinal studies with drop-out," Biometrika, Biometrika Trust, vol. 103(3), pages 683-700.
    6. Jae Kwang Kim, 2011. "Parametric fractional imputation for missing data analysis," Biometrika, Biometrika Trust, vol. 98(1), pages 119-132.
    7. J. Molina & A. Rotnitzky & M. Sued & J. M. Robins, 2017. "Multiple robustness in factorized likelihood models," Biometrika, Biometrika Trust, vol. 104(3), pages 561-581.
    8. Sixia Chen & Jae kwang Kim, 2017. "Semiparametric fractional imputation using empirical likelihood in survey sampling," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(1), pages 69-81, January.
    9. Sixia Chen & David Haziza, 2017. "Multiply robust imputation procedures for the treatment of item nonresponse in surveys," Biometrika, Biometrika Trust, vol. 104(2), pages 439-453.
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