IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v16y2020icp108-120.html
   My bibliography  Save this article

Semiparametric inference with missing data: Robustness to outliers and model misspecification

Author

Listed:
  • Cantoni, Eva
  • de Luna, Xavier

Abstract

Classical semiparametric inference with missing outcome data is not robust to contamination of the observed data and a single observation can have arbitrarily large influence on estimation of a parameter of interest. This sensitivity is exacerbated when inverse probability weighting methods are used, which may overweight contaminated observations. Inverse probability weighted, double robust and outcome regression estimators of location and scale parameters are introduced, which are robust to contamination in the sense that their influence function is bounded. Asymptotic properties are deduced and finite sample behaviour studied. Simulated experiments show that contamination can be more serious a threat to the quality of inference than model misspecification. An interesting aspect of the results is that the auxiliary outcome model used to adjust for ignorable missingness by some of the estimators, is also useful to protect against contamination. Both adjustment to ignorable missingness and protection against contamination are achieved through weighting schemes. A case study illustrates how the resulting weights can be studied to gain insights on how the two different weighting schemes interact.

Suggested Citation

  • Cantoni, Eva & de Luna, Xavier, 2020. "Semiparametric inference with missing data: Robustness to outliers and model misspecification," Econometrics and Statistics, Elsevier, vol. 16(C), pages 108-120.
  • Handle: RePEc:eee:ecosta:v:16:y:2020:i:c:p:108-120
    DOI: 10.1016/j.ecosta.2020.01.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306220300198
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles

    File URL: https://libkey.io/10.1016/j.ecosta.2020.01.003?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

    for a different version of it.

    References listed on IDEAS

    as
    1. José R. Zubizarreta, 2015. "Stable Weights that Balance Covariates for Estimation With Incomplete Outcome Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 910-922, September.
    2. Zhelonkin, Mikhail & Genton, Marc G. & Ronchetti, Elvezio, 2012. "On the robustness of two-stage estimators," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 726-732.
    3. Gruber Susan & van der Laan Mark J., 2010. "An Application of Collaborative Targeted Maximum Likelihood Estimation in Causal Inference and Genomics," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-31, May.
    4. J.-F. Beaumont & D. Haziza & A. Ruiz-Gazen, 2013. "A unified approach to robust estimation in finite population sampling," Biometrika, Biometrika Trust, vol. 100(3), pages 555-569.
    5. Kosuke Imai & Marc Ratkovic, 2014. "Covariate balancing propensity score," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 243-263, January.
    6. Zhiqiang Tan, 2010. "Bounded, efficient and doubly robust estimation with inverse weighting," Biometrika, Biometrika Trust, vol. 97(3), pages 661-682.
    7. Cantoni E. & Ronchetti E., 2001. "Robust Inference for Generalized Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1022-1030, September.
    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. Lee, Seong-ho & Ma, Yanyuan & de Luna, Xavier, 2025. "Covariate balancing for causal inference on categorical and continuous treatments," Econometrics and Statistics, Elsevier, vol. 33(C), pages 304-329.
    2. Naghi, Andrea A. & Váradi, Máté & Zhelonkin, Mikhail, 2025. "Robust Estimation of Probit Models with Endogeneity," Econometrics and Statistics, Elsevier, vol. 34(C), pages 78-90.
    3. Lafférs, Lukáš & Nedela, Roman, 2025. "Sensitivity of Bounds on ATEs under Survey Nonresponse," Econometrics and Statistics, Elsevier, vol. 34(C), pages 1-13.

    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. Shixiao Zhang & Peisong Han & Changbao Wu, 2023. "Calibration Techniques Encompassing Survey Sampling, Missing Data Analysis and Causal Inference," International Statistical Review, International Statistical Institute, vol. 91(2), pages 165-192, August.
    2. 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.
    3. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    4. Dasom Lee & Shu Yang & Lin Dong & Xiaofei Wang & Donglin Zeng & Jianwen Cai, 2023. "Improving trial generalizability using observational studies," Biometrics, The International Biometric Society, vol. 79(2), pages 1213-1225, June.
    5. Chen, Shanting & Mallory, Allen B., 2021. "The effect of racial discrimination on mental and physical health: A propensity score weighting approach," Social Science & Medicine, Elsevier, vol. 285(C).
    6. Susan Athey & Guido W. Imbens, 2017. "The State of Applied Econometrics: Causality and Policy Evaluation," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 3-32, Spring.
    7. Sven Klaassen & Jan Rabenseifner & Jannis Kueck & Philipp Bach, 2025. "Calibration Strategies for Robust Causal Estimation: Theoretical and Empirical Insights on Propensity Score-Based Estimators," Papers 2503.17290, arXiv.org, revised May 2025.
    8. repec:kan:wpaper:202315 is not listed on IDEAS
    9. Lee, Seong-ho & Ma, Yanyuan & de Luna, Xavier, 2025. "Covariate balancing for causal inference on categorical and continuous treatments," Econometrics and Statistics, Elsevier, vol. 33(C), pages 304-329.
    10. Vahe Avagyan & Stijn Vansteelandt, 2021. "Stable inverse probability weighting estimation for longitudinal studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 1046-1067, September.
    11. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2021. "Synthetic Difference-in-Differences," American Economic Review, American Economic Association, vol. 111(12), pages 4088-4118, December.
    12. Dongcheng Zhang & Kunpeng Zhang, 2020. "Weighting-Based Treatment Effect Estimation via Distribution Learning," Papers 2012.13805, arXiv.org, revised May 2023.
    13. Xu, Wenfu & Tan, Zhiqiang, 2024. "High-dimensional model-assisted inference for treatment effects with multi-valued treatments," Journal of Econometrics, Elsevier, vol. 244(1).
    14. Jason J. Sauppe & Sheldon H. Jacobson, 2017. "The role of covariate balance in observational studies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(4), pages 323-344, June.
    15. Kallus Nathan & Santacatterina Michele, 2021. "Optimal balancing of time-dependent confounders for marginal structural models," Journal of Causal Inference, De Gruyter, vol. 9(1), pages 345-369, January.
    16. Wu Xue & Xiaoke Zhang & Kwun Chuen Gary Chan & Raymond K. W. Wong, 2024. "RKHS-based covariate balancing for survival causal effect estimation," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 30(1), pages 34-58, January.
    17. Hengfang Wang & Jae Kwang Kim, 2025. "Information projection approach to smoothed propensity score weighting for handling selection bias under missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 77(1), pages 127-153, February.
    18. Yimin Dai & Ying Yan, 2024. "Mahalanobis balancing: A multivariate perspective on approximate covariate balancing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(4), pages 1450-1471, December.
    19. Michael Zimmert, 2018. "The Finite Sample Performance of Treatment Effects Estimators based on the Lasso," Papers 1805.05067, arXiv.org.
    20. 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.
    21. Noémi Kreif & Richard Grieve & Iván Díaz & David Harrison, 2015. "Evaluation of the Effect of a Continuous Treatment: A Machine Learning Approach with an Application to Treatment for Traumatic Brain Injury," Health Economics, John Wiley & Sons, Ltd., vol. 24(9), pages 1213-1228, September.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:ecosta:v:16:y:2020:i:c:p:108-120. 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: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.