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On classification with nonignorable missing data

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  • Mojirsheibani, Majid

Abstract

We consider the problem of kernel classification with nonignorable missing data. Instead of imposing a fully parametric model for the selection probability, which can be quite sensitive to the violations of model assumptions, here we consider a semiparametric exponential tilting selection probability model in the spirit of Kim and Yu (2011). In addition to the existing parameter estimators, we also develop some new estimators of the unknown components of the model that are particularly suitable for classification problems. We also study various strong optimality properties of the proposed kernel-type classifiers.

Suggested Citation

  • Mojirsheibani, Majid, 2021. "On classification with nonignorable missing data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jmvana:v:184:y:2021:i:c:s0047259x21000336
    DOI: 10.1016/j.jmva.2021.104755
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    References listed on IDEAS

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    1. Puying Zhao & Lei Wang & Jun Shao, 2019. "Empirical likelihood and Wilks phenomenon for data with nonignorable missing values," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(4), pages 1003-1024, December.
    2. Majid Mojirsheibani & Timothy Reese, 2017. "Kernel regression estimation for incomplete data with applications," Statistical Papers, Springer, vol. 58(1), pages 185-209, March.
    3. Jun Shao & Lei Wang, 2016. "Semiparametric inverse propensity weighting for nonignorable missing data," Biometrika, Biometrika Trust, vol. 103(1), pages 175-187.
    4. Morikawa, Kosuke & Kano, Yutaka, 2018. "Identification problem of transition models for repeated measurement data with nonignorable missing values," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 216-230.
    5. Morikawa, Kosuke & Kim, Jae Kwang, 2018. "A note on the equivalence of two semiparametric estimation methods for nonignorable nonresponse," Statistics & Probability Letters, Elsevier, vol. 140(C), pages 1-6.
    6. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    7. Timothy Reese & Majid Mojirsheibani, 2017. "On the $$L_p$$ L p norms of kernel regression estimators for incomplete data with applications to classification," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 81-112, March.
    8. Kim, Jae Kwang & Yu, Cindy Long, 2011. "A Semiparametric Estimation of Mean Functionals With Nonignorable Missing Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 157-165.
    9. Noh, Hohsuk & El Ghouch, Anouar & Bouezmarni, Taoufik, 2013. "Copula-Based Regression Estimation and Inference," LIDAM Reprints ISBA 2013045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    10. Arnab Kumar Maity & Vivek Pradhan & Ujjwal Das, 2019. "Bias Reduction in Logistic Regression with Missing Responses When the Missing Data Mechanism is Nonignorable," The American Statistician, Taylor & Francis Journals, vol. 73(4), pages 340-349, October.
    11. Hohsuk Noh & Anouar El Ghouch & Taoufik Bouezmarni, 2013. "Copula-Based Regression Estimation and Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 676-688, June.
    12. Mauricio Sadinle & Jerome P Reiter, 2019. "Sequentially additive nonignorable missing data modelling using auxiliary marginal information," Biometrika, Biometrika Trust, vol. 106(4), pages 889-911.
    13. 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.
    14. Jiwei Zhao & Jun Shao, 2015. "Semiparametric Pseudo-Likelihoods in Generalized Linear Models With Nonignorable Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1577-1590, December.
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    Cited by:

    1. 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.

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