IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v210y2025ics0047259x25000600.html

Random projection-based response best-subset selector for ultra-high dimensional multivariate data

Author

Listed:
  • Hu, Jianhua
  • Li, Tao
  • Liu, Xiaoqian
  • Liu, Xu

Abstract

In this article, we propose a random projection-based response best-subset selector to perform response variable selection in ultra-high dimensional multivariate data, where both the dimensions of response and predictor variables are substantially greater than the sample size. This method is developed by integrating the response best-subset selector and random projection technique which is applied to reduce dimensionality of predictors. Under a multivariate tail eigenvalue condition, such a random projection-based dimensionality reduction of predictors only leads to an ignorable error between the original and dimension-reduced models. A computational procedure is presented. The proposed method exhibits model consistency under some certain conditions. The efficiency and merit of the proposed method are strongly supported by extensive finite-sample simulation studies. A real breast cancer dataset spanning 22 chromosomes are analyzed to demonstrate the proposed method.

Suggested Citation

  • Hu, Jianhua & Li, Tao & Liu, Xiaoqian & Liu, Xu, 2025. "Random projection-based response best-subset selector for ultra-high dimensional multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 210(C).
    • Handle: RePEc:eee:jmvana:v:210:y:2025:i:c:s0047259x25000600
    DOI: 10.1016/j.jmva.2025.105465
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X25000600
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2025.105465?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhong, Ping-Shou & Chen, Song Xi, 2011. "Tests for High-Dimensional Regression Coefficients With Factorial Designs," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 260-274.
    2. Jianhua Hu & Jian Huang & Xiaoqian Liu & Xu Liu, 2023. "Response best-subset selector for multivariate regression with high-dimensional response variables," Biometrika, Biometrika Trust, vol. 110(1), pages 205-223.
    3. Z. Su & G. Zhu & X. Chen & Y. Yang, 2016. "Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression," Biometrika, Biometrika Trust, vol. 103(3), pages 579-593.
    4. Timothy I. Cannings & Richard J. Samworth, 2017. "Random-projection ensemble classification," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 959-1035, September.
    5. Hu, Jianhua & Liu, Xiaoqian & Liu, Xu & Xia, Ningning, 2022. "Some aspects of response variable selection and estimation in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. X Liu & S Zheng & X Feng, 2020. "Estimation of error variance via ridge regression," Biometrika, Biometrika Trust, vol. 107(2), pages 481-488.
    7. Chengchun Shi & Wenbin Lu & Rui Song, 2020. "A Sparse Random Projection-Based Test for Overall Qualitative Treatment Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1201-1213, July.
    8. Changyu Liu & Xingqiu Zhao & Jian Huang, 2024. "A Random Projection Approach to Hypothesis Tests in High-Dimensional Single-Index Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 1008-1018, April.
    9. Yanming Li & Bin Nan & Ji Zhu, 2015. "Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure," Biometrics, The International Biometric Society, vol. 71(2), pages 354-363, June.
    10. Kate Lawrenson & Siddhartha Kar & Karen McCue & Karoline Kuchenbaeker & Kyriaki Michailidou & Jonathan Tyrer & Jonathan Beesley & Susan J. Ramus & Qiyuan Li & Melissa K. Delgado & Janet M. Lee & Krist, 2016. "Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast–ovarian cancer susceptibility locus," Nature Communications, Nature, vol. 7(1), pages 1-22, November.
    11. Kun Chen & Kung‐Sik Chan & Nils Chr. Stenseth, 2012. "Reduced rank stochastic regression with a sparse singular value decomposition," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 74(2), pages 203-221, March.
    12. Kun Chen & Hongbo Dong & Kung-Sik Chan, 2013. "Reduced rank regression via adaptive nuclear norm penalization," Biometrika, Biometrika Trust, vol. 100(4), pages 901-920.
    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. Hu, Jianhua & Liu, Xiaoqian & Liu, Xu & Xia, Ningning, 2022. "Some aspects of response variable selection and estimation in multivariate linear regression," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    2. Guo, Wenxing & Balakrishnan, Narayanaswamy & He, Mu, 2023. "Envelope-based sparse reduced-rank regression for multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    3. Kohei Yoshikawa & Shuichi Kawano, 2023. "Sparse reduced-rank regression for simultaneous rank and variable selection via manifold optimization," Computational Statistics, Springer, vol. 38(1), pages 53-75, March.
    4. S. Yaser Samadi & Wiranthe B. Herath, 2023. "Reduced-rank Envelope Vector Autoregressive Models," Papers 2309.12902, arXiv.org.
    5. Luo, Chongliang & Liang, Jian & Li, Gen & Wang, Fei & Zhang, Changshui & Dey, Dipak K. & Chen, Kun, 2018. "Leveraging mixed and incomplete outcomes via reduced-rank modeling," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 378-394.
    6. Feng, Sanying & Lian, Heng & Zhu, Fukang, 2016. "Reduced rank regression with possibly non-smooth criterion functions: An empirical likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 139-150.
    7. Mishra, Aditya & Dey, Dipak K. & Chen, Yong & Chen, Kun, 2021. "Generalized co-sparse factor regression," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    8. Yang, Yuehan & Xia, Siwei & Yang, Hu, 2023. "Multivariate sparse Laplacian shrinkage for joint estimation of two graphical structures," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    9. Zhao, Weihua & Jiang, Xuejun & Lian, Heng, 2018. "A principal varying-coefficient model for quantile regression: Joint variable selection and dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 269-280.
    10. Marie Levakova & Susanne Ditlevsen, 2024. "Penalisation Methods in Fitting High‐Dimensional Cointegrated Vector Autoregressive Models: A Review," International Statistical Review, International Statistical Institute, vol. 92(2), pages 160-193, August.
    11. Goh, Gyuhyeong & Dey, Dipak K. & Chen, Kun, 2017. "Bayesian sparse reduced rank multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 14-28.
    12. Lian, Heng & Kim, Yongdai, 2016. "Nonconvex penalized reduced rank regression and its oracle properties in high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 383-393.
    13. Chen, Canyi & Xu, Wangli & Zhu, Liping, 2022. "Distributed estimation in heterogeneous reduced rank regression: With application to order determination in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    14. Dennis Cook, R. & Forzani, Liliana, 2023. "On the role of partial least squares in path analysis for the social sciences," Journal of Business Research, Elsevier, vol. 167(C).
    15. Bergsma, Wicher P, 2020. "Regression with I-priors," Econometrics and Statistics, Elsevier, vol. 14(C), pages 89-111.
    16. Yaohua Hu & Jian Lu & Xiaoqi Yang & Kai Zhang, 2025. "Iterative mix thresholding algorithm with continuation technique for mix sparse optimization and application," Journal of Global Optimization, Springer, vol. 91(3), pages 511-534, March.
    17. Nayiri Galestian Pour & Soudabeh Shemehsavar, 2024. "Learning from high dimensional data based on weighted feature importance in decision tree ensembles," Computational Statistics, Springer, vol. 39(1), pages 313-342, February.
    18. Lee, Hwiyoung & Ye, Zhenyao & Chen, Chixiang & Kochunov, Peter & Hong, L. Elliot & Chen, Shuo, 2026. "Fast autoregressive model for multivariate dependent outcomes with application to lipidomics analysis for Alzheimer’s disease and APOE-ε4," Computational Statistics & Data Analysis, Elsevier, vol. 215(C).
    19. Ziwen Gao & Jiahui Zou & Xinyu Zhang & Yanyuan Ma, 2023. "Frequentist model averaging for envelope models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1325-1364, September.
    20. Wang, Yihe & Zhao, Sihai Dave, 2021. "A nonparametric empirical Bayes approach to large-scale multivariate regression," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:jmvana:v:210:y:2025:i:c:s0047259x25000600. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.