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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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. 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).
    2. 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.
    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.

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