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Model-free feature screening for ultrahigh-dimensional data conditional on some variables

Author

Listed:
  • Yi Liu

    (Chinese Academy of Sciences
    China University of Petroleum)

  • Qihua Wang

    (Chinese Academy of Sciences
    Shenzhen University)

Abstract

In this paper, the conditional distance correlation (CDC) is used as a measure of correlation to develop a conditional feature screening procedure given some significant variables for ultrahigh-dimensional data. The proposed procedure is model free and is called conditional distance correlation-sure independence screening (CDC-SIS for short). That is, we do not specify any model structure between the response and the predictors, which is appealing in some practical problems of ultrahigh-dimensional data analysis. The sure screening property of the CDC-SIS is proved and a simulation study was conducted to evaluate the finite sample performances. Real data analysis is used to illustrate the proposed method. The results indicate that CDC-SIS performs well.

Suggested Citation

  • Yi Liu & Qihua Wang, 2018. "Model-free feature screening for ultrahigh-dimensional data conditional on some variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 283-301, April.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:2:d:10.1007_s10463-016-0597-2
    DOI: 10.1007/s10463-016-0597-2
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    References listed on IDEAS

    as
    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.
    2. 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.
    3. 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.
    4. 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.
    5. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    6. 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.
    7. Xueqin Wang & Wenliang Pan & Wenhao Hu & Yuan Tian & Heping Zhang, 2015. "Conditional Distance Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1726-1734, December.
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    Cited by:

    1. Xiaochao Xia & Hao Ming, 2022. "A Flexibly Conditional Screening Approach via a Nonparametric Quantile Partial Correlation," Mathematics, MDPI, vol. 10(24), pages 1-32, December.
    2. Jing Zhang & Yanyan Liu & Hengjian Cui, 2021. "Model-free feature screening via distance correlation for ultrahigh dimensional survival data," Statistical Papers, Springer, vol. 62(6), pages 2711-2738, December.
    3. Jing Zhang & Haibo Zhou & Yanyan Liu & Jianwen Cai, 2021. "Conditional screening for ultrahigh-dimensional survival data in case-cohort studies," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(4), pages 632-661, October.

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