IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v128y2018icp242-254.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301476
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2018.06.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Ming-Yen Cheng & Toshio Honda & Jin-Ting Zhang, 2016. "Forward Variable Selection for Sparse Ultra-High Dimensional Varying Coefficient Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(515), pages 1209-1221, July.
    6. 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.
    7. Lin, Lu & Sun, Jing, 2016. "Adaptive conditional feature screening," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 287-301.
    8. Ma, Xuejun & Zhang, Jingxiao, 2016. "Robust model-free feature screening via quantile correlation," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 472-480.
    9. 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.
    10. 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.
    11. Li, Xingxiang & Cheng, Guosheng & Wang, Liming & Lai, Peng & Song, Fengli, 2017. "Ultrahigh dimensional feature screening via projection," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 88-104.
    12. 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.
    13. 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.
    14. Clifford M. Hurvich & Jeffrey S. Simonoff & Chih‐Ling Tsai, 1998. "Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 271-293.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Jun Lu & Dan Wang & Qinqin Hu, 2022. "Interaction screening via canonical correlation," Computational Statistics, Springer, vol. 37(5), pages 2637-2670, November.
    2. Ping Wang & Lu Lin, 2023. "Conditional characteristic feature screening for massive imbalanced data," Statistical Papers, Springer, vol. 64(3), pages 807-834, June.
    3. Lu, Jun & Lin, Lu & Wang, WenWu, 2021. "Partition-based feature screening for categorical data via RKHS embeddings," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akira Shinkyu, 2023. "Forward Selection for Feature Screening and Structure Identification in Varying Coefficient Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 485-511, February.
    2. Zhang, Shen & Zhao, Peixin & Li, Gaorong & Xu, Wangli, 2019. "Nonparametric independence screening for ultra-high dimensional generalized varying coefficient models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 37-52.
    3. Yi Chu & Lu Lin, 2020. "Conditional SIRS for nonparametric and semiparametric models by marginal empirical likelihood," Statistical Papers, Springer, vol. 61(4), pages 1589-1606, August.
    4. Jun Lu & Lu Lin, 2020. "Model-free conditional screening via conditional distance correlation," Statistical Papers, Springer, vol. 61(1), pages 225-244, February.
    5. Zhang, Shucong & Zhou, Yong, 2018. "Variable screening for ultrahigh dimensional heterogeneous data via conditional quantile correlations," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 1-13.
    6. Dai, Linlin & Chen, Kani & Sun, Zhihua & Liu, Zhenqiu & Li, Gang, 2018. "Broken adaptive ridge regression and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 334-351.
    7. Liming Wang & Xingxiang Li & Xiaoqing Wang & Peng Lai, 2022. "Unified mean-variance feature screening for ultrahigh-dimensional regression," Computational Statistics, Springer, vol. 37(4), pages 1887-1918, September.
    8. Yang, Guangren & Zhang, Ling & Li, Runze & Huang, Yuan, 2019. "Feature screening in ultrahigh-dimensional varying-coefficient Cox model," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 284-297.
    9. Randall Reese & Guifang Fu & Geran Zhao & Xiaotian Dai & Xiaotian Li & Kenneth Chiu, 2022. "Epistasis Detection via the Joint Cumulant," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 514-532, December.
    10. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    11. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    12. Zhang, Shucong & Pan, Jing & Zhou, Yong, 2018. "Robust conditional nonparametric independence screening for ultrahigh-dimensional data," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 95-101.
    13. Xiaolin Chen & Xiaojing Chen & Yi Liu, 2019. "A note on quantile feature screening via distance correlation," Statistical Papers, Springer, vol. 60(5), pages 1741-1762, October.
    14. Guo, Chaohui & Lv, Jing & Wu, Jibo, 2021. "Composite quantile regression for ultra-high dimensional semiparametric model averaging," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    15. Xi Wu & Shifeng Xiong & Weiyan Mu, 2023. "An Ensemble Method for Feature Screening," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    16. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    17. Haofeng Wang & Hongxia Jin & Xuejun Jiang & Jingzhi Li, 2022. "Model Selection for High Dimensional Nonparametric Additive Models via Ridge Estimation," Mathematics, MDPI, vol. 10(23), pages 1-22, December.
    18. Yang, Baoying & Yin, Xiangrong & Zhang, Nan, 2019. "Sufficient variable selection using independence measures for continuous response," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 480-493.
    19. 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.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:128:y:2018:i:c:p:242-254. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.