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Semiparametric double robust and efficient estimation for mean functionals with response missing at random

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  • Guo, Xu
  • Fang, Yun
  • Zhu, Xuehu
  • Xu, Wangli
  • Zhu, Lixing

Abstract

Under dimension reduction structure, several semiparametric estimators for the mean of missing response are proposed, which can efficiently deal with the dimensionality problem. Specifically, a generalized version of Augmented Inverse Probability Weighting estimator (AIPW) is proposed and its double robustness, estimation consistency and asymptotic efficiency are investigated. A generalized version of Inverse Probability Weighting (IPW) estimator is also introduced. An asymptotic efficiency reduction phenomenon occurs in the sense that the IPW estimator with the true selection probability is asymptotically less efficient than the one with an estimated selection probability. Besides, two partial imputation and two complete imputation estimators are discussed. We further systematically investigate the comparisons among these estimators in theory. Several simulation studies and a real data analysis are conducted for performance examination and illustration.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:325-339
    DOI: 10.1016/j.csda.2018.07.017
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    3. Niwen Zhou & Xu Guo & Lixing Zhu, 2022. "The role of propensity score structure in asymptotic efficiency of estimated conditional quantile treatment effect," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 718-743, June.
    4. Ao Yuan & Anqi Yin & Ming T. Tan, 2021. "Enhanced Doubly Robust Procedure for Causal Inference," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(3), pages 454-478, December.

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