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Unified mean-variance feature screening for ultrahigh-dimensional regression

Author

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  • Liming Wang

    (Nanjing University of Finance and Economics Hongshan College
    Nanjing University of Information Science and Technology)

  • Xingxiang Li

    (Xi’an Jiaotong University)

  • Xiaoqing Wang

    (Nanjing University of Finance and Economics)

  • Peng Lai

    (Nanjing University of Information Science and Technology)

Abstract

Feature screening is a popular and efficient statistical technique in processing ultrahigh-dimensional data. When a regression model consists both categorical and continuous predictors, a unified feature screening procedure is needed. Thus, we propose a unified mean-variance sure independence screening (UMV-SIS) for this setup. The mean-variance (MV), an effective utility to measure the dependence between two random variables, is widely used in feature screening for discriminant analysis. In this paper, we advocate using the kernel smoothing method to estimate MV between two continuous variables, thereby extending it to screen categorical and continuous predictors simultaneously. Besides the uniformity for screening, UMV-SIS is a model-free procedure without any specification of a regression model; this broadens the scope of its application. In theory, we show that the UMV-SIS procedure has the sure screening and ranking consistency properties under mild conditions. To solve some difficulties in marginal feature screening for linear model and further enhance the screening performance of our proposed method, an iterative UMV-SIS procedure is developed. The promising performances of the new method are supported by extensive numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:37:y:2022:i:4:d:10.1007_s00180-021-01184-2
    DOI: 10.1007/s00180-021-01184-2
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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. 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. 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.
    5. Efang Kong & Yingcun Xia & Wei Zhong, 2019. "Composite Coefficient of Determination and Its Application in Ultrahigh Dimensional Variable Screening," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1740-1751, October.
    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. 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.
    8. Yan, Xiaodong & Tang, Niansheng & Xie, Jinhan & Ding, Xianwen & Wang, Zhiqiang, 2018. "Fused mean–variance filter for feature screening," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 18-32.
    9. 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.
    10. 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.
    11. 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.
    12. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, 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. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    15. 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.
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    1. Jingxuan Luo & Lili Yue & Gaorong Li, 2023. "Overview of High-Dimensional Measurement Error Regression Models," Mathematics, MDPI, vol. 11(14), pages 1-22, July.

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