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Semiparametric inverse propensity weighting for nonignorable missing data

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  • Jun Shao
  • Lei Wang

Abstract

To estimate unknown population parameters based on data having nonignorable missing values with a semiparametric exponential tilting propensity, Kim & Yu (2011) assumed that the tilting parameter is known or can be estimated from external data, in order to avoid the identifiability issue. To remove this serious limitation on the methodology, we use an instrument, i.e., a covariate related to the study variable but unrelated to the missing data propensity, to construct some estimating equations. Because these estimating equations are semiparametric, we profile the nonparametric component using a kernel-type estimator and then estimate the tilting parameter based on the profiled estimating equations and the generalized method of moments. Once the tilting parameter is estimated, so is the propensity, and then other population parameters can be estimated using the inverse propensity weighting approach. Consistency and asymptotic normality of the proposed estimators are established. The finite-sample performance of the estimators is studied through simulation, and a real-data example is also presented.

Suggested Citation

  • Jun Shao & Lei Wang, 2016. "Semiparametric inverse propensity weighting for nonignorable missing data," Biometrika, Biometrika Trust, vol. 103(1), pages 175-187.
  • Handle: RePEc:oup:biomet:v:103:y:2016:i:1:p:175-187.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv071
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    References listed on IDEAS

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    1. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    2. Sheng Wang & Jun Shao & Jae Kwang Kim, "undated". "An Instrumental Variable Approach for Identification and Estimation with Nonignorable Nonresponse," Mathematica Policy Research Reports a9593fac2c9746f486d2162f9, Mathematica Policy Research.
    3. repec:mpr:mprres:8160 is not listed on IDEAS
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    Cited by:

    1. Tianqing Liu & Xiaohui Yuan, 2020. "Doubly robust augmented-estimating-equations estimation with nonignorable nonresponse data," Statistical Papers, Springer, vol. 61(6), pages 2241-2270, December.
    2. Bian, Yuan & Yi, Grace Y. & He, Wenqing, 2024. "A unified framework of analyzing missing data and variable selection using regularized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).
    3. Li, Mengyan & Ma, Yanyuan & Zhao, Jiwei, 2022. "Efficient estimation in a partially specified nonignorable propensity score model," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    4. Deng, Jianqiu & Yang, Xiaojie & Wang, Qihua, 2022. "Surrogate space based dimension reduction for nonignorable nonresponse," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    5. Lyu Ni & Jun Shao, 2023. "Estimation with multivariate outcomes having nonignorable item nonresponse," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(1), pages 1-15, February.
    6. 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).
    7. Tang, Cheng Yong, 2024. "A model specification test for semiparametric nonignorable missing data modeling," Econometrics and Statistics, Elsevier, vol. 30(C), pages 124-132.
    8. Lei Wang & Wei Ma, 2021. "Improved empirical likelihood inference and variable selection for generalized linear models with longitudinal nonignorable dropouts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 623-647, June.
    9. Guo, Xu & Song, Lianlian & Fang, Yun & Zhu, Lixing, 2019. "Model checking for general linear regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 1-12.
    10. Zhang, Ting & Wang, Lei, 2020. "Smoothed empirical likelihood inference and variable selection for quantile regression with nonignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    11. Zhang, Jing & Wang, Qihua & Kang, Jian, 2020. "Feature screening under missing indicator imputation with non-ignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    12. Rui Duan & C. Jason Liang & Pamela Shaw & Cheng Yong Tang & Yong Chen, 2020. "Missing at Random or Not: A Semiparametric Testing Approach," Papers 2003.11181, arXiv.org.
    13. Bindele, Huybrechts F. & Nguelifack, Brice M., 2019. "Generalized signed-rank estimation for regression models with non-ignorable missing responses," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 14-33.
    14. 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.
    15. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.
    16. Jierui Du & Xia Cui, 2024. "Semiparametric estimation in generalized additive partial linear models with nonignorable nonresponse data," Statistical Papers, Springer, vol. 65(5), pages 3235-3259, July.
    17. Majid Mojirsheibani, 2022. "On the maximal deviation of kernel regression estimators with NMAR response variables," Statistical Papers, Springer, vol. 63(5), pages 1677-1705, October.
    18. Aiai Yu & Yujie Zhong & Xingdong Feng & Ying Wei, 2023. "Quantile regression for nonignorable missing data with its application of analyzing electronic medical records," Biometrics, The International Biometric Society, vol. 79(3), pages 2036-2049, September.
    19. Xianwen Ding & Jiandong Chen & Xueping Chen, 2020. "Regularized quantile regression for ultrahigh-dimensional data with nonignorable missing responses," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(5), pages 545-568, July.
    20. Shonosuke Sugasawa & Kosuke Morikawa & Keisuke Takahata, 2022. "Bayesian semiparametric modeling of response mechanism for nonignorable missing data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 101-117, March.
    21. Mojirsheibani, Majid, 2021. "On classification with nonignorable missing data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    22. Pengfei Li & Jing Qin & Yukun Liu, 2023. "Instability of inverse probability weighting methods and a remedy for nonignorable missing data," Biometrics, The International Biometric Society, vol. 79(4), pages 3215-3226, December.
    23. Zhan Liu & Chun Yip Yau, 2022. "A propensity score adjustment method for longitudinal time series models under nonignorable nonresponse," Statistical Papers, Springer, vol. 63(1), pages 317-342, February.
    24. Jingxuan Guo & Fuguo Liu & Wolfgang Karl Härdle & Xueliang Zhang & Kai Wang & Ting Zeng & Liping Yang & Maozai Tian, 2023. "Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression," Mathematics, MDPI, vol. 11(24), pages 1-30, December.

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