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Sure Independence Screening for Ultrahigh-Dimensional Additive Model with Multivariate Response

Author

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  • Yongshuai Chen

    (School of Statistics, Capital University of Economics and Business, Beijing 100070, China)

  • Baosheng Liang

    (Department of Biostatistics, School of Public Health, Peking University, Beijing 100191, China)

Abstract

This paper investigated an ultrahigh-dimensional feature screening approach for additive models with multivariate responses. We proposed a nonparametric screening procedure based on random vector correlations between each predictor and multivariate response, and we established the theoretical results of sure screening and ranking consistency properties under regularity conditions. We also developed an iterative sure independence screening algorithm for convenient and efficient implementation. Extensive finite-sample simulations and a real data example demonstrate the superiority of the proposed procedure over 58–100% of existing candidates. On average, the proposed method outperforms 79% of existing methods across all scenarios considered.

Suggested Citation

  • Yongshuai Chen & Baosheng Liang, 2025. "Sure Independence Screening for Ultrahigh-Dimensional Additive Model with Multivariate Response," Mathematics, MDPI, vol. 13(10), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1558-:d:1652155
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    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. 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.
    3. Hyonho Chun & Sündüz Keleş, 2010. "Sparse partial least squares regression for simultaneous dimension reduction and variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 3-25, January.
    4. Zhentao Tian & Tingyu Lai & Zhongzhan Zhang, 2025. "Variation of conditional mean and its application in ultrahigh dimensional feature screening," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(2), pages 352-382, January.
    5. 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.
    6. Shuaishuai Chen & Jun Lu, 2023. "Quantile-Composited Feature Screening for Ultrahigh-Dimensional Data," Mathematics, MDPI, vol. 11(10), pages 1-21, May.
    7. 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)

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