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Estimation of mean response via the effective balancing score

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  • Zonghui Hu
  • Dean A. Follmann
  • Naisyin Wang

Abstract

We introduce the effective balancing score for estimation of the mean response under a missing-at-random mechanism. Unlike conventional balancing scores, the proposed score is constructed via dimension reduction free of model specification. Three types of such scores are introduced, distinguished by whether they carry the covariate information about the missingness, the response, or both. The effective balancing score leads to consistent estimation with little or no loss in efficiency. Compared to existing estimators, it reduces the burden of model specification and is more robust. It is a near-automatic procedure which is most appealing when high-dimensional covariates are involved. We investigate its asymptotic and numerical properties, and illustrate its application with an HIV disease study.

Suggested Citation

  • Zonghui Hu & Dean A. Follmann & Naisyin Wang, 2014. "Estimation of mean response via the effective balancing score," Biometrika, Biometrika Trust, vol. 101(3), pages 613-624.
    • Handle: RePEc:oup:biomet:v:101:y:2014:i:3:p:613-624.
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    File URL: http://hdl.handle.net/10.1093/biomet/asu022
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    Cited by:

    1. Wang, Lei & Zhao, Puying & Shao, Jun, 2021. "Dimension-reduced semiparametric estimation of distribution functions and quantiles with nonignorable nonresponse," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    2. Lee, Myoung-jae & Lee, Sanghyeok, 2019. "Double robustness without weighting," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 175-180.
    3. Guo, Xu & Fang, Yun & Zhu, Xuehu & Xu, Wangli & Zhu, Lixing, 2018. "Semiparametric double robust and efficient estimation for mean functionals with response missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 325-339.
    4. Lei Wang, 2019. "Dimension reduction for kernel-assisted M-estimators with missing response at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(4), pages 889-910, August.
    5. Ming-Yueh Huang & Kwun Chuen Gary Chan, 2017. "Joint sufficient dimension reduction and estimation of conditional and average treatment effects," Biometrika, Biometrika Trust, vol. 104(3), pages 583-596.

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