IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v60y2019i5d10.1007_s00362-017-0894-8.html
   My bibliography  Save this article

A note on quantile feature screening via distance correlation

Author

Listed:
  • Xiaolin Chen

    (Qufu Normal University)

  • Xiaojing Chen

    (Qufu Normal University)

  • Yi Liu

    (China University of Petroleum)

Abstract

In this paper, we propose a new feature screening procedure based on a robust quantile version of distance correlation with some desirable characters. First, it is particularly useful for data exhibiting heterogeneity, which is very common for high dimensional data. Second, it is robust to model misspecification and behaves reliably when some of features contain outliers or follow heavy-tailed distributions. Under very mild conditions, we have established its sure screening property. In practice, a same index set is often found to be adequate by the quantile analysis. So we furthermore present a composite robust quantile version of distance correlation to perform feature screening. Simulation studies are carried out to examine the performance of advised procedures. We also illustrate them by a real data example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0894-8
    DOI: 10.1007/s00362-017-0894-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-017-0894-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-017-0894-8?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 J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    3. Xiaofeng Shao & Jingsi Zhang, 2014. "Martingale Difference Correlation and Its Use in High-Dimensional Variable Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1302-1318, September.
    4. Guodong Li & Yang Li & Chih-Ling Tsai, 2015. "Quantile Correlations and Quantile Autoregressive Modeling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 246-261, March.
    5. Dengke Xu & Zhongzhan Zhang & Liucang Wu, 2014. "Variable selection in high-dimensional double generalized linear models," Statistical Papers, Springer, vol. 55(2), pages 327-347, May.
    6. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    7. Yuanshan Wu & Guosheng Yin, 2015. "Conditional quantile screening in ultrahigh-dimensional heterogeneous data," Biometrika, Biometrika Trust, vol. 102(1), pages 65-76.
    8. 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.
    9. 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.
    10. Junying Zhang & Riquan Zhang & Zhiping Lu, 2016. "Quantile-adaptive variable screening in ultra-high dimensional varying coefficient models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(4), pages 643-654, March.
    11. Lin, Lu & Sun, Jing & Zhu, Lixing, 2013. "Nonparametric feature screening," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 162-174.
    12. Ma, Xuejun & Zhang, Jingxiao, 2016. "Robust model-free feature screening via quantile correlation," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 472-480.
    13. 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.
    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. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.
    2. Lu, Shuiyun & Chen, Xiaolin & Xu, Sheng & Liu, Chunling, 2020. "Joint model-free feature screening for ultra-high dimensional semi-competing risks data," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    3. 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.

    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. 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.
    2. 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).
    3. Zhong, Wei & Wang, Jiping & Chen, Xiaolin, 2021. "Censored mean variance sure independence screening for ultrahigh dimensional survival data," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    4. 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.
    5. 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.
    6. 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.
    7. Chen, Xiaolin & Chen, Xiaojing & Wang, Hong, 2018. "Robust feature screening for ultra-high dimensional right censored data via distance correlation," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 118-138.
    8. Min Chen & Yimin Lian & Zhao Chen & Zhengjun Zhang, 2017. "Sure explained variability and independence screening," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 849-883, October.
    9. 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.
    10. Craig, Sarah J.C. & Kenney, Ana M. & Lin, Junli & Paul, Ian M. & Birch, Leann L. & Savage, Jennifer S. & Marini, Michele E. & Chiaromonte, Francesca & Reimherr, Matthew L. & Makova, Kateryna D., 2023. "Constructing a polygenic risk score for childhood obesity using functional data analysis," Econometrics and Statistics, Elsevier, vol. 25(C), pages 66-86.
    11. Ma, Xuejun & Zhang, Jingxiao, 2016. "Robust model-free feature screening via quantile correlation," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 472-480.
    12. 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.
    13. 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.
    14. Jun Lu & Lu Lin, 2020. "Model-free conditional screening via conditional distance correlation," Statistical Papers, Springer, vol. 61(1), pages 225-244, February.
    15. 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.
    16. 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.
    17. He, Yong & Zhang, Liang & Ji, Jiadong & Zhang, Xinsheng, 2019. "Robust feature screening for elliptical copula regression model," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 568-582.
    18. 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.
    19. Jing Zhang & Guosheng Yin & Yanyan Liu & Yuanshan Wu, 2018. "Censored cumulative residual independent screening for ultrahigh-dimensional survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(2), pages 273-292, April.
    20. Xia, Xiaochao & Yang, Hu & Li, Jialiang, 2016. "Feature screening for generalized varying coefficient models with application to dichotomous responses," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 85-97.

    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:spr:stpapr:v:60:y:2019:i:5:d:10.1007_s00362-017-0894-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.