IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i22p4685-d1282669.html
   My bibliography  Save this article

Optimal Non-Asymptotic Bounds for the Sparse β Model

Author

Listed:
  • Xiaowei Yang

    (College of Mathematics, Sichuan University, Chengdu 610017, China)

  • Lu Pan

    (Department of Statistics, Central China Normal University, Wuhan 430079, China)

  • Kun Cheng

    (School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100080, China)

  • Chao Liu

    (College of Economics, Shenzhen University, Shenzhen 518060, China)

Abstract

This paper investigates the sparse β model with 𝓁 1 penalty in the field of network data models, which is a hot topic in both statistical and social network research. We present a refined algorithm designed for parameter estimation in the proposed model. Its effectiveness is highlighted through its alignment with the proximal gradient descent method, stemming from the convexity of the loss function. We study the estimation consistency and establish an optimal bound for the proposed estimator. Empirical validations facilitated through meticulously designed simulation studies corroborate the efficacy of our methodology. These assessments highlight the prospective contributions of our methodology to the advanced field of network data analysis.

Suggested Citation

  • Xiaowei Yang & Lu Pan & Kun Cheng & Chao Liu, 2023. "Optimal Non-Asymptotic Bounds for the Sparse β Model," Mathematics, MDPI, vol. 11(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4685-:d:1282669
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/22/4685/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/22/4685/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jing Luo & Tour Liu & Jing Wu & Sailan Waleed Ahmed Ali, 2022. "Asymptotic in undirected random graph models with a noisy degree sequence," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(3), pages 789-810, February.
    2. Mingli Chen & Kengo Kato & Chenlei Leng, 2021. "Analysis of networks via the sparse β‐model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(5), pages 887-910, 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. Qiuping Wang & Yuan Zhang & Ting Yan, 2023. "Asymptotic theory in network models with covariates and a growing number of node parameters," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(2), pages 369-392, April.

    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:11:y:2023:i:22:p:4685-:d:1282669. 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.