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Feature screening via false discovery rate control for linear model with multivariate responses

Author

Listed:
  • Congran Yu

    (Beijing Polytechnic)

  • Hengjian Cui

    (Capital Normal University)

Abstract

We develop a novel feature selection method for linear regression with multivariate responses in ultrahigh-dimensional data analysis. This method is constructed under the framework of False Discovery Rate (FDR) control for multiple testing, and it employs a multiple data-splitting strategy. In each splitting, the data is divided into two disjoint parts. The first part is utilized for feature screening based on R-Vector (RV) correlation, and multiple testing is then conducted on the selected features for both parts. The z-values of the statistics are aggregated to control the FDR, and the set of important features is determined by rejecting the null hypotheses. The asymptotic theory of FDR control for this method is established under mild conditions. Additionally, we evaluate the finite sample performance of our feature selection procedure through Monte Carlo simulations. Finally, we apply this approach to detect important human genes associated with psychological well-being.

Suggested Citation

  • Congran Yu & Hengjian Cui, 2025. "Feature screening via false discovery rate control for linear model with multivariate responses," Statistical Papers, Springer, vol. 66(2), pages 1-29, February.
  • Handle: RePEc:spr:stpapr:v:66:y:2025:i:2:d:10.1007_s00362-025-01661-6
    DOI: 10.1007/s00362-025-01661-6
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    References listed on IDEAS

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    1. Guo, Wenwen & Cui, Hengjian, 2019. "Projection tests for high-dimensional spiked covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 21-32.
    2. Lilun Du & Xu Guo & Wenguang Sun & Changliang Zou, 2023. "False Discovery Rate Control Under General Dependence By Symmetrized Data Aggregation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(541), pages 607-621, January.
    3. Yaowu Liu & Jun Xie, 2020. "Cauchy Combination Test: A Powerful Test With Analytic p-Value Calculation Under Arbitrary Dependency Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 393-402, January.
    4. 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.
    5. 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.
    6. 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.
    7. Chenguang Dai & Buyu Lin & Xin Xing & Jun S. Liu, 2023. "False Discovery Rate Control via Data Splitting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 118(544), pages 2503-2520, October.
    8. Congran Yu & Wenwen Guo & Xinyuan Song & Hengjian Cui, 2023. "Feature screening with latent responses," Biometrics, The International Biometric Society, vol. 79(2), pages 878-890, June.
    9. Meinshausen, Nicolai & Meier, Lukas & Bühlmann, Peter, 2009. "p-Values for High-Dimensional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1671-1681.
    10. 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.
    11. 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.
    12. John D. Storey & Jonathan E. Taylor & David Siegmund, 2004. "Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 187-205, February.
    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.
    14. 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.
    15. Nicolai Meinshausen, 2015. "Group bound: confidence intervals for groups of variables in sparse high dimensional regression without assumptions on the design," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(5), pages 923-945, November.
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