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Feature screening for multi-response varying coefficient models with ultrahigh dimensional predictors

Author

Listed:
  • Lu, Jun
  • Lin, Lu

Abstract

This article investigates the feature screening procedure for multivariate response varying coefficient linear models. A new conditional canonical correlation coefficient is proposed to characterize the correlation between each predictor and the multivariate response. It is shown that the proposed method is more powerful to distinguish the informative features from the noises than the existing competitors, especially for the case of high-dimensional response. The ranking consistency and the sure screening property are established for the new method. Meanwhile, an iterative version of the feature screening procedure is also introduced. Both the numerical simulations and real data analysis are conducted to illustrate the effectiveness of our method.

Suggested Citation

  • Lu, Jun & Lin, Lu, 2018. "Feature screening for multi-response varying coefficient models with ultrahigh dimensional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 242-254.
  • Handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:242-254
    DOI: 10.1016/j.csda.2018.06.009
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    References listed on IDEAS

    as
    1. Lin, Lu & Sun, Jing, 2016. "Adaptive conditional feature screening," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 287-301.
    2. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    3. 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.
    4. 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.
    5. Jianqing Fan & Yunbei Ma & Wei Dai, 2014. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Varying Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1270-1284, September.
    6. Ma, Xuejun & Zhang, Jingxiao, 2016. "Robust model-free feature screening via quantile correlation," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 472-480.
    7. Wang, Hansheng, 2009. "Forward Regression for Ultra-High Dimensional Variable Screening," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1512-1524.
    8. Wang, Hansheng & Xia, Yingcun, 2009. "Shrinkage Estimation of the Varying Coefficient Model," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 747-757.
    9. Chen Xu & Jiahua Chen, 2014. "The Sparse MLE for Ultrahigh-Dimensional Feature Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1257-1269, September.
    10. repec:taf:jnlasa:v:111:y:2016:i:515:p:1209-1221 is not listed on IDEAS
    11. Qinqin Hu & Lu Lin, 2017. "Conditional sure independence screening by conditional marginal empirical likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 63-96, February.
    12. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    13. repec:eee:csdana:v:114:y:2017:i:c:p:88-104 is not listed on IDEAS
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