IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v167y2022ics0167947321002036.html
   My bibliography  Save this article

Projection quantile correlation and its use in high-dimensional grouped variable screening

Author

Listed:
  • Liu, Jicai
  • Si, Yuefeng
  • Niu, Yong
  • Zhang, Riquan

Abstract

In this paper, we propose a new measure, called Projection Quantile Correlation (PQC), to detect quantile dependence between a response and multivariate predictors at a given quantile level. The PQC measure is free of tuning parameters, robust against heavy tailed distributions and outliers, and does not require moment conditions on the predictors. We obtain theoretical properties of the PQC and its empirical counterpart. We then use the measure to select the grouped predictors that contribute to the conditional quantile of the response for high-dimensional data with group structures. We also establish sure independent screening properties for the group screening method. We illustrate the finite sample performance of the proposed method through simulations and an application to a dataset.

Suggested Citation

  • Liu, Jicai & Si, Yuefeng & Niu, Yong & Zhang, Riquan, 2022. "Projection quantile correlation and its use in high-dimensional grouped variable screening," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:csdana:v:167:y:2022:i:c:s0167947321002036
    DOI: 10.1016/j.csda.2021.107369
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947321002036
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2021.107369?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. Patrick Breheny, 2015. "The group exponential lasso for bi‐level variable selection," Biometrics, The International Biometric Society, vol. 71(3), pages 731-740, September.
    2. Hengjian Cui & Runze Li & Wei Zhong, 2015. "Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 630-641, June.
    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. Conde-Amboage, Mercedes & Sánchez-Sellero, César & González-Manteiga, Wenceslao, 2015. "A lack-of-fit test for quantile regression models with high-dimensional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 128-138.
    5. Jian Huang & Shuange Ma & Huiliang Xie & Cun-Hui Zhang, 2009. "A group bridge approach for variable selection," Biometrika, Biometrika Trust, vol. 96(2), pages 339-355.
    6. Bierens, Herman J., 1982. "Consistent model specification tests," Journal of Econometrics, Elsevier, vol. 20(1), pages 105-134, October.
    7. 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.
    8. 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.
    9. Escanciano, J. Carlos, 2006. "A Consistent Diagnostic Test For Regression Models Using Projections," Econometric Theory, Cambridge University Press, vol. 22(6), pages 1030-1051, December.
    10. Jordi Barretina & Giordano Caponigro & Nicolas Stransky & Kavitha Venkatesan & Adam A. Margolin & Sungjoon Kim & Christopher J.Wilson & Joseph Lehár & Gregory V. Kryukov & Dmitriy Sonkin & Anupama Red, 2012. "Addendum: The Cancer Cell Line Encyclopedia enables predictive modelling of anticancer drug sensitivity," Nature, Nature, vol. 492(7428), pages 290-290, December.
    11. Yuanshan Wu & Guosheng Yin, 2015. "Conditional quantile screening in ultrahigh-dimensional heterogeneous data," Biometrika, Biometrika Trust, vol. 102(1), pages 65-76.
    12. Zhao, Sihai Dave & Li, Yi, 2012. "Principled sure independence screening for Cox models with ultra-high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 397-411.
    13. Jordi Barretina & Giordano Caponigro & Nicolas Stransky & Kavitha Venkatesan & Adam A. Margolin & Sungjoon Kim & Christopher J. Wilson & Joseph Lehár & Gregory V. Kryukov & Dmitriy Sonkin & Anupama Re, 2012. "The Cancer Cell Line Encyclopedia enables predictive modelling of anticancer drug sensitivity," Nature, Nature, vol. 483(7391), pages 603-607, March.
    14. Baringhaus, L. & Franz, C., 2004. "On a new multivariate two-sample test," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 190-206, January.
    15. Xingdong Feng & Xuming He & Jianhua Hu, 2011. "Wild bootstrap for quantile regression," Biometrika, Biometrika Trust, vol. 98(4), pages 995-999.
    16. Zhu, Li-Xing & Fang, Kai-Tai & Bhatti, M Ishaq, 1997. "On Estimated Projection Pursuit-Type Crámer-von Mises Statistics, ," Journal of Multivariate Analysis, Elsevier, vol. 63(1), pages 1-14, October.
    17. Jian Kang & Hyokyoung G Hong & Yi Li, 2017. "Partition-based ultrahigh-dimensional variable screening," Biometrika, Biometrika Trust, vol. 104(4), pages 785-800.
    18. Liping Zhu & Kai Xu & Runze Li & Wei Zhong, 2017. "Projection correlation between two random vectors," Biometrika, Biometrika Trust, vol. 104(4), pages 829-843.
    19. 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.
    20. Yong Niu & Riquan Zhang & Jicai Liu & Huapeng Li, 2020. "Group screening for ultra-high-dimensional feature under linear model," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 4(1), pages 43-54, July.
    21. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    Full references (including those not matched with items on IDEAS)

    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. Qiu, Debin & Ahn, Jeongyoun, 2020. "Grouped variable screening for ultra-high dimensional data for linear model," Computational Statistics & Data Analysis, Elsevier, vol. 144(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. Xin-Bing Kong & Zhi Liu & Yuan Yao & Wang Zhou, 2017. "Sure screening by ranking the canonical correlations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 46-70, March.
    5. 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.
    6. 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.
    7. 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).
    8. Xu, Kai & Zhou, Yeqing, 2021. "Projection-averaging-based cumulative covariance and its use in goodness-of-fit testing for single-index models," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    9. Jing Zhang & Qihua Wang & Xuan Wang, 2022. "Surrogate-variable-based model-free feature screening for survival data under the general censoring mechanism," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(2), pages 379-397, April.
    10. Loann David Denis Desboulets, 2018. "A Review on Variable Selection in Regression Analysis," Econometrics, MDPI, vol. 6(4), pages 1-27, November.
    11. Zhang, Jing & Wang, Qihua & Kang, Jian, 2020. "Feature screening under missing indicator imputation with non-ignorable missing response," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    12. Li, Lu & Ke, Chenlu & Yin, Xiangrong & Yu, Zhou, 2023. "Generalized martingale difference divergence: Detecting conditional mean independence with applications in variable screening," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    13. 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.
    14. 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.
    15. Ke, Chenlu & Yang, Wei & Yuan, Qingcong & Li, Lu, 2023. "Partial sufficient variable screening with categorical controls," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    16. 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.
    17. Ping Wang & Lu Lin, 2023. "Conditional characteristic feature screening for massive imbalanced data," Statistical Papers, Springer, vol. 64(3), pages 807-834, June.
    18. Park, Seyoung & Kim, Hyunjin & Lee, Eun Ryung, 2023. "Regional quantile regression for multiple responses," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
    19. 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.
    20. Baiguo An & Guozhong Feng & Jianhua Guo, 2022. "Interaction Identification and Clique Screening for Classification with Ultra-high Dimensional Discrete Features," Journal of Classification, Springer;The Classification Society, vol. 39(1), pages 122-146, March.

    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:167:y:2022:i:c:s0167947321002036. 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.