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How to Make Model†free Feature Screening Approaches for Full Data Applicable to the Case of Missing Response?

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  • Qihua Wang
  • Yongjin Li

Abstract

It is quite a challenge to develop model†free feature screening approaches for missing response problems because the existing standard missing data analysis methods cannot be applied directly to high dimensional case. This paper develops some novel methods by borrowing information of missingness indicators such that any feature screening procedures for ultrahigh†dimensional covariates with full data can be applied to missing response case. The first method is the so†called missing indicator imputation screening, which is developed by proving that the set of the active predictors of interest for the response is a subset of the active predictors for the product of the response and missingness indicator under some mild conditions. As an alternative, another method called Venn diagram†based approach is also developed. The sure screening property is proven for both methods. It is shown that the complete case analysis can also keep the sure screening property of any feature screening approach with sure screening property.

Suggested Citation

  • Qihua Wang & Yongjin Li, 2018. "How to Make Model†free Feature Screening Approaches for Full Data Applicable to the Case of Missing Response?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(2), pages 324-346, June.
    • Handle: RePEc:bla:scjsta:v:45:y:2018:i:2:p:324-346
    DOI: 10.1111/sjos.12290
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    Cited by:

    1. 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).
    2. Yuting Wei & Qihua Wang & Wei Liu, 2021. "Model averaging for linear models with responses missing at random," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 535-553, June.
    3. 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.
    4. Tang, Niansheng & Xia, Linli & Yan, Xiaodong, 2019. "Feature screening in ultrahigh-dimensional partially linear models with missing responses at random," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 208-227.
    5. Adriano Zanin Zambom & Gregory J. Matthews, 2021. "Sure independence screening in the presence of missing data," Statistical Papers, Springer, vol. 62(2), pages 817-845, April.

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