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Robust model selection with covariables missing at random

Author

Listed:
  • Zhongqi Liang

    (Zhejiang Gongshang University)

  • Qihua Wang

    (Zhejiang Gongshang University
    Academy of Mathematics and Systems Science, Chinese Academy of Sciences)

  • Yuting Wei

    (Universtiy of Science and Technology of China)

Abstract

Let $$f_{Y|X,Z}(y|x,z)$$ f Y | X , Z ( y | x , z ) be the conditional probability function of Y given (X, Z), where Y is the scalar response variable, while (X, Z) is the covariable vector. This paper proposes a robust model selection criterion for $$f_{Y|X,Z}(y|x,z)$$ f Y | X , Z ( y | x , z ) with X missing at random. The proposed method is developed based on a set of assumed models for the selection probability function. However, the consistency of model selection by our proposal does not require these models to be correctly specified, while it only requires that the selection probability function is a function of these assumed selective probability functions. Under some conditions, it is proved that the model selection by the proposed method is consistent and the estimator for population parameter vector is consistent and asymptotically normal. A Monte Carlo study was conducted to evaluate the finite-sample performance of our proposal. A real data analysis was used to illustrate the practical application of our proposal.

Suggested Citation

  • Zhongqi Liang & Qihua Wang & Yuting Wei, 2022. "Robust model selection with covariables missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 539-557, June.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:3:d:10.1007_s10463-021-00806-2
    DOI: 10.1007/s10463-021-00806-2
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    References listed on IDEAS

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    1. Gerda Claeskens & Fabrizio Consentino, 2008. "Variable Selection with Incomplete Covariate Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1062-1069, December.
    2. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models 2 volume set," Cambridge Books, Cambridge University Press, number 9780521478373, July.
    3. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521477444.
    4. Ibrahim, Joseph G. & Zhu, Hongtu & Tang, Niansheng, 2008. "Model Selection Criteria for Missing-Data Problems Using the EM Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1648-1658.
    5. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258.
    6. Wang, Qihua & Su, Miaomiao & Wang, Ruoyu, 2021. "A beyond multiple robust approach for missing response problem," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    7. Craig A. Rolling & Yuhong Yang, 2014. "Model selection for estimating treatment effects," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(4), pages 749-769, September.
    8. Jiming Jiang & Thuan Nguyen & J. Sunil Rao, 2015. "The E-MS Algorithm: Model Selection With Incomplete Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1136-1147, September.
    9. Xinyu Zhang & Haiying Wang & Yanyuan Ma & Raymond J. Carroll, 2017. "Linear Model Selection When Covariates Contain Errors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1553-1561, October.
    10. Andrew Gelman & Iven Van Mechelen & Geert Verbeke & Daniel F. Heitjan & Michel Meulders, 2005. "Multiple Imputation for Model Checking: Completed-Data Plots with Missing and Latent Data," Biometrics, The International Biometric Society, vol. 61(1), pages 74-85, March.
    11. Claeskens G. & Hjort N.L., 2003. "The Focused Information Criterion," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 900-916, January.
    12. Wei, Yuting & Wang, Qihua & Duan, Xiaogang & Qin, Jing, 2021. "Bias-corrected Kullback–Leibler distance criterion based model selection with covariables missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    13. Qin Shao & Lijian Yang, 2017. "Oracally efficient estimation and consistent model selection for auto-regressive moving average time series with trend," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 507-524, March.
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