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Semiparametric dimension reduction estimation for mean response with missing data

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  • Zonghui Hu
  • Dean A. Follmann
  • Jing Qin

Abstract

Model misspecification can be a concern for high-dimensional data. Nonparametric regression obviates model specification but is impeded by the curse of dimensionality. This paper focuses on the estimation of the marginal mean response when there is missingness in the response and multiple covariates are available. We propose estimating the mean response through nonparametric functional estimation, where the dimension is reduced by a parametric working index. The proposed semiparametric estimator is robust to model misspecification: it is consistent for any working index if the missing mechanism of the response is known or correctly specified up to unknown parameters; even with misspecification in the missing mechanism, it is consistent so long as the working index can recover E(Y | X), the conditional mean response given the covariates. In addition, when the missing mechanism is correctly specified, the semiparametric estimator attains the optimal efficiency if E(Y | X) is recoverable through the working index. Robustness and efficiency of the proposed estimator is further investigated by simulations. We apply the proposed method to a clinical trial for HIV. Copyright 2010, Oxford University Press.

Suggested Citation

  • Zonghui Hu & Dean A. Follmann & Jing Qin, 2010. "Semiparametric dimension reduction estimation for mean response with missing data," Biometrika, Biometrika Trust, vol. 97(2), pages 305-319.
    • Handle: RePEc:oup:biomet:v:97:y:2010:i:2:p:305-319
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    File URL: http://hdl.handle.net/10.1093/biomet/asq005
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    Cited by:

    1. Xu, Hong-Xia & Fan, Guo-Liang & Chen, Zhen-Long, 2017. "Hypothesis tests in partial linear errors-in-variables models with missing response," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 219-229.
    2. Qihua Wang & Tao Zhang & Wolfgang Karl Härdle, 2016. "An Extended Single-index Model with Missing Response at Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1140-1152, December.
    3. Qihua Wang & Tao Zhang & Wolfgang Karl Härdle, 2014. "An Extended Single Index Model with Missing Response at Random," SFB 649 Discussion Papers SFB649DP2014-003, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Effraimidis, Georgios & Dahl, Christian M., 2013. "Nonparametric Estimation of Cumulative Incidence Functions for Competing Risks Data with Missing Cause of Failure," Discussion Papers on Economics 21/2013, University of Southern Denmark, Department of Economics.
    5. Fan, Guo-Liang & Xu, Hong-Xia & Liang, Han-Ying, 2019. "Dimension reduction estimation for central mean subspace with missing multivariate response," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    6. Chen, Songxi, 2013. "Mann-Whitney Test with Adjustments to Pre-treatment Variables for Missing Values and Observational Study," MPRA Paper 46239, University Library of Munich, Germany.
    7. Guo, Xu & Wang, Tao & Xu, Wangli & Zhu, Lixing, 2014. "Dimension reduction with missing response at random," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 228-242.

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