IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v128y2018icp325-339.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794731830183X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.07.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. van der Laan Mark J., 2010. "Targeted Maximum Likelihood Based Causal Inference: Part II," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-33, February.
    2. Weihua Cao & Anastasios A. Tsiatis & Marie Davidian, 2009. "Improving efficiency and robustness of the doubly robust estimator for a population mean with incomplete data," Biometrika, Biometrika Trust, vol. 96(3), pages 723-734.
    3. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    4. van der Laan Mark J. & Rubin Daniel, 2006. "Targeted Maximum Likelihood Learning," The International Journal of Biostatistics, De Gruyter, vol. 2(1), pages 1-40, December.
    5. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    6. Xue, Liugen, 2009. "Empirical likelihood for linear models with missing responses," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1353-1366, August.
    7. 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.
    8. Jinyong Hahn, 1998. "On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects," Econometrica, Econometric Society, vol. 66(2), pages 315-332, March.
    9. Xia, Yingcun, 2006. "Asymptotic Distributions For Two Estimators Of The Single-Index Model," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1112-1137, December.
    10. M. Hristache & V. Patilea, 2017. "Conditional moment models with data missing at random," Biometrika, Biometrika Trust, vol. 104(3), pages 735-742.
    11. van der Laan Mark J., 2010. "Targeted Maximum Likelihood Based Causal Inference: Part I," The International Journal of Biostatistics, De Gruyter, vol. 6(2), pages 1-45, February.
    12. Xue, Liugen & Xue, Dong, 2011. "Empirical likelihood for semiparametric regression model with missing response data," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 723-740, April.
    13. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
    14. Rubin Daniel B & van der Laan Mark J., 2008. "Empirical Efficiency Maximization: Improved Locally Efficient Covariate Adjustment in Randomized Experiments and Survival Analysis," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-40, May.
    15. Li, Lexin & Lu, Wenbin, 2008. "Sufficient Dimension Reduction With Missing Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 822-831, June.
    16. Liugen Xue, 2009. "Empirical Likelihood Confidence Intervals for Response Mean with Data Missing at Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 671-685, December.
    17. Ding, Xiaobo & Wang, Qihua, 2011. "Fusion-Refinement Procedure for Dimension Reduction With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1193-1207.
    18. Tan Zhiqiang, 2008. "Comment: Improved Local Efficiency and Double Robustness," The International Journal of Biostatistics, De Gruyter, vol. 4(1), pages 1-9, June.
    19. 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.
    20. 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.
    21. Zonghui Hu & Dean A. Follmann & Jing Qin, 2012. "Semiparametric Double Balancing Score Estimation for Incomplete Data With Ignorable Missingness," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 247-257, March.
    22. Wei Lin & K. B. Kulasekera, 2007. "Identifiability of single-index models and additive-index models," Biometrika, Biometrika Trust, vol. 94(2), pages 496-501.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Ash Abebe & Huybrechts F. Bindele & Masego Otlaadisa & Boikanyo Makubate, 2021. "Robust estimation of single index models with responses missing at random," Statistical Papers, Springer, vol. 62(5), pages 2195-2225, October.
    4. Wei Luo, 2022. "On efficient dimension reduction with respect to the interaction between two response variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 269-294, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wang, Qihua & Su, Miaomiao & Wang, Ruoyu, 2021. "A beyond multiple robust approach for missing response problem," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    2. Jianxuan Liu & Yanyuan Ma & Lan Wang, 2018. "An alternative robust estimator of average treatment effect in causal inference," Biometrics, The International Biometric Society, vol. 74(3), pages 910-923, September.
    3. Iván Díaz & Elizabeth Colantuoni & Daniel F. Hanley & Michael Rosenblum, 2019. "Improved precision in the analysis of randomized trials with survival outcomes, without assuming proportional hazards," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 439-468, July.
    4. Zhiwei Zhang & Zhen Chen & James F. Troendle & Jun Zhang, 2012. "Causal Inference on Quantiles with an Obstetric Application," Biometrics, The International Biometric Society, vol. 68(3), pages 697-706, September.
    5. Jie Zhou & Zhiwei Zhang & Zhaohai Li & Jun Zhang, 2015. "Coarsened Propensity Scores and Hybrid Estimators for Missing Data and Causal Inference," International Statistical Review, International Statistical Institute, vol. 83(3), pages 449-471, December.
    6. Lee, Myoung-jae & Lee, Sanghyeok, 2019. "Double robustness without weighting," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 175-180.
    7. Xue, Liugen & Zhang, Jinghua, 2020. "Empirical likelihood for partially linear single-index models with missing observations," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    8. Michael Zimmert, 2018. "The Finite Sample Performance of Treatment Effects Estimators based on the Lasso," Papers 1805.05067, arXiv.org.
    9. Kwun Chuen Gary Chan & Sheung Chi Phillip Yam & Zheng Zhang, 2016. "Globally efficient non-parametric inference of average treatment effects by empirical balancing calibration weighting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(3), pages 673-700, June.
    10. Zhao, Hui & Zhao, Pu-Ying & Tang, Nian-Sheng, 2013. "Empirical likelihood inference for mean functionals with nonignorably missing response data," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 101-116.
    11. Susan Athey & Guido W. Imbens & Stefan Wager, 2018. "Approximate residual balancing: debiased inference of average treatment effects in high dimensions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(4), pages 597-623, September.
    12. Luo, Yu & Graham, Daniel J. & McCoy, Emma J., 2023. "Semiparametric Bayesian doubly robust causal estimation," LSE Research Online Documents on Economics 117944, London School of Economics and Political Science, LSE Library.
    13. Su, Miaomiao & Wang, Qihua, 2022. "A convex programming solution based debiased estimator for quantile with missing response and high-dimensional covariables," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    14. Frölich, Markus & Huber, Martin & Wiesenfarth, Manuel, 2017. "The finite sample performance of semi- and non-parametric estimators for treatment effects and policy evaluation," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 91-102.
    15. Xue, Liugen & Xue, Dong, 2011. "Empirical likelihood for semiparametric regression model with missing response data," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 723-740, April.
    16. Chris Muris, 2020. "Efficient GMM Estimation with Incomplete Data," The Review of Economics and Statistics, MIT Press, vol. 102(3), pages 518-530, July.
    17. Mireille E. Schnitzer & Erica E.M. Moodie & Mark J. van der Laan & Robert W. Platt & Marina B. Klein, 2014. "Modeling the impact of hepatitis C viral clearance on end-stage liver disease in an HIV co-infected cohort with targeted maximum likelihood estimation," Biometrics, The International Biometric Society, vol. 70(1), pages 144-152, March.
    18. Difang Huang & Jiti Gao & Tatsushi Oka, 2022. "Semiparametric Single-Index Estimation for Average Treatment Effects," Papers 2206.08503, arXiv.org, revised Oct 2022.
    19. Han, Peisong, 2012. "A note on improving the efficiency of inverse probability weighted estimator using the augmentation term," Statistics & Probability Letters, Elsevier, vol. 82(12), pages 2221-2228.
    20. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:325-339. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.