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Robust composite weighted quantile screening for ultrahigh dimensional discriminant analysis

Author

Listed:
  • Fengli Song

    (Nanjing University of Information Science and Technology)

  • Peng Lai

    (Nanjing University of Information Science and Technology)

  • Baohua Shen

    (Nanjing University of Information Science and Technology)

Abstract

This paper is concerned with feature screening for the ultrahigh dimensional discriminant analysis. A new feature screening procedure based on the conditional quantile is proposed. The proposed procedure has some desirable features. First, it is model-free which does not require specific discriminant model and can be directly applied to the multi-categories situation. Second, it is robust against heavy-tailed distributions, potential outliers and the sample shortage for some categories, which are very common for high dimensional data. We establish the sure screening property and ranking consistency property of the proposed procedure under some regular conditions. Simulation studies and a real data example are used to assess its finite sample performance.

Suggested Citation

  • Fengli Song & Peng Lai & Baohua Shen, 2020. "Robust composite weighted quantile screening for ultrahigh dimensional discriminant analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(7), pages 799-820, October.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:7:d:10.1007_s00184-019-00758-x
    DOI: 10.1007/s00184-019-00758-x
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    References listed on IDEAS

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    1. Jingyuan Liu & Runze Li & Rongling Wu, 2014. "Feature Selection for Varying Coefficient Models With Ultrahigh-Dimensional Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 266-274, March.
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    3. Rui Pan & Hansheng Wang & Runze Li, 2016. "Ultrahigh-Dimensional Multiclass Linear Discriminant Analysis by Pairwise Sure Independence Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 169-179, March.
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    6. Runze Li & Wei Zhong & Liping Zhu, 2012. "Feature Screening via Distance Correlation Learning," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1129-1139, September.
    7. Lai, Peng & Song, Fengli & Chen, Kaiwen & Liu, Zhi, 2017. "Model free feature screening with dependent variable in ultrahigh dimensional binary classification," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 141-148.
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