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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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