IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v142y2020ics0167947319301665.html
   My bibliography  Save this article

Generalized ℓ1-penalized quantile regression with linear constraints

Author

Listed:
  • Liu, Yongxin
  • Zeng, Peng
  • Lin, Lu

Abstract

In many application areas, prior subject matter knowledge can be formulated as constraints on parameters in order to get a more accurate fit. A generalized ℓ1-penalized quantile regression with linear constraints on parameters is considered, including either linear inequality or equality constraints or both. It allows a general form of penalization, including the usual lasso, the fused lasso and the adaptive lasso as special cases. The KKT conditions of the optimization problem are derived and the whole solution path is computed as a function of the tuning parameter. A formula for the number of degrees of freedom is derived, which is used to construct model selection criteria for selecting optimal tuning parameters. Finally, several simulation studies and two real data examples are presented to illustrate the proposed method.

Suggested Citation

  • Liu, Yongxin & Zeng, Peng & Lin, Lu, 2020. "Generalized ℓ1-penalized quantile regression with linear constraints," Computational Statistics & Data Analysis, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:csdana:v:142:y:2020:i:c:s0167947319301665
    DOI: 10.1016/j.csda.2019.106819
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947319301665
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2019.106819?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 search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiaofei Wu & Rongmei Liang & Hu Yang, 2022. "Penalized and constrained LAD estimation in fixed and high dimension," Statistical Papers, Springer, vol. 63(1), pages 53-95, February.

    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:csdana:v:142:y:2020:i:c:s0167947319301665. 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.

    We have no bibliographic references for this item. You can help adding them by using 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/locate/csda .

    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.