IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3758-d1532258.html
   My bibliography  Save this article

Efficient Estimation and Response Variable Selection in Sparse Partial Envelope Model

Author

Listed:
  • Yu Wu

    (Business School, Nanjing University, Nanjing 210093, China
    These authors contributed equally to this work.)

  • Jing Zhang

    (College of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
    These authors contributed equally to this work.)

Abstract

In this paper, we propose a sparse partial envelope model that performs response variable selection efficiently under the partial envelope model. We discuss its theoretical properties including consistency, an oracle property and the asymptotic distribution of the sparse partial envelope estimator. A large-sample situation and high-dimensional situation are both considered. Numerical experiments demonstrate that the sparse partial envelope estimator has excellent response variable selection performance both in the large-sample situation and the high-dimensional situation. Moreover, simulation studies and real data analysis suggest that the sparse partial envelope estimator has a much more competitive performance than the standard estimator, the oracle partial envelope estimator, the active partial envelope estimator and the sparse envelope estimator, whether it is in the large-sample situation or the high-dimensional situation.

Suggested Citation

  • Yu Wu & Jing Zhang, 2024. "Efficient Estimation and Response Variable Selection in Sparse Partial Envelope Model," Mathematics, MDPI, vol. 12(23), pages 1-28, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3758-:d:1532258
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3758/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/23/3758/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zhihua Su & R. Dennis Cook, 2012. "Inner envelopes: efficient estimation in multivariate linear regression," Biometrika, Biometrika Trust, vol. 99(3), pages 687-702.
    2. 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.
    3. Aldrin, Magne, 1996. "Moderate projection pursuit regression for multivariate response data," Computational Statistics & Data Analysis, Elsevier, vol. 21(5), pages 501-531, May.
    4. Zhihua Su & R. Dennis Cook, 2011. "Partial envelopes for efficient estimation in multivariate linear regression," Biometrika, Biometrika Trust, vol. 98(1), pages 133-146.
    5. Yuqing Pan & Qing Mai & Xin Zhang, 2019. "Covariate-Adjusted Tensor Classification in High Dimensions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1305-1319, July.
    6. Cook, R. Dennis & Forzani, Liliana & Su, Zhihua, 2016. "A note on fast envelope estimation," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 42-54.
    7. R. D. Cook & I. S. Helland & Z. Su, 2013. "Envelopes and partial least squares regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 851-877, November.
    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. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    2. Yue Zhao & Ingrid Van Keilegom & Shanshan Ding, 2022. "Envelopes for censored quantile regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1562-1585, December.
    3. D. J. Eck & R. D. Cook, 2017. "Weighted envelope estimation to handle variability in model selection," Biometrika, Biometrika Trust, vol. 104(3), pages 743-749.
    4. Alexander M. Franks, 2022. "Reducing subspace models for large‐scale covariance regression," Biometrics, The International Biometric Society, vol. 78(4), pages 1604-1613, December.
    5. Iaci, Ross & Yin, Xiangrong & Zhu, Lixing, 2016. "The Dual Central Subspaces in dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 178-189.
    6. Yeonhee Park & Zhihua Su & Hongtu Zhu, 2017. "Groupwise envelope models for imaging genetic analysis," Biometrics, The International Biometric Society, vol. 73(4), pages 1243-1253, December.
    7. Jain Yashita & Ding Shanshan & Qiu Jing, 2019. "Sliced inverse regression for integrative multi-omics data analysis," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 18(1), pages 1-13, February.
    8. 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).
    9. Lan Liu & Wei Li & Zhihua Su & Dennis Cook & Luca Vizioli & Essa Yacoub, 2022. "Efficient estimation via envelope chain in magnetic resonance imaging‐based studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 481-501, June.
    10. R. D. Cook & I. S. Helland & Z. Su, 2013. "Envelopes and partial least squares regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 851-877, November.
    11. Lasanthi C. R. Pelawa Watagoda & David J. Olive, 2021. "Comparing six shrinkage estimators with large sample theory and asymptotically optimal prediction intervals," Statistical Papers, Springer, vol. 62(5), pages 2407-2431, October.
    12. 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).
    13. May, Paul & Biesecker, Matthew & Rekabdarkolaee, Hossein Moradi, 2022. "Response envelopes for linear coregionalization models," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    14. Zhang, Xin & Wang, Chong & Wu, Yichao, 2018. "Functional envelope for model-free sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 37-50.
    15. Cook, R. Dennis & Forzani, Liliana & Su, Zhihua, 2016. "A note on fast envelope estimation," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 42-54.
    16. 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).
    17. Cook, R. Dennis & Su, Zhihua & Yang, Yi, 2015. "envlp: A MATLAB Toolbox for Computing Envelope Estimators in Multivariate Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 62(i08).
    18. Li, Gen & Yang, Dan & Nobel, Andrew B. & Shen, Haipeng, 2016. "Supervised singular value decomposition and its asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 7-17.
    19. S. Yaser Samadi & Wiranthe B. Herath, 2023. "Reduced-rank Envelope Vector Autoregressive Models," Papers 2309.12902, arXiv.org.
    20. Cook, R. Dennis, 2022. "A slice of multivariate dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

    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:gam:jmathe:v:12:y:2024:i:23:p:3758-:d:1532258. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.