IDEAS home Printed from https://ideas.repec.org/a/taf/lstaxx/v46y2017i21p10897-10902.html
   My bibliography  Save this article

The Frisch–Waugh–Lovell theorem for the lasso and the ridge regression

Author

Listed:
  • Hiroshi Yamada

Abstract

The Frisch–Waugh–Lovell (FWL) (partitioned regression) theorem is essential in regression analysis. This is partly because it is quite useful to derive theoretical results. The lasso regression and the ridge regression, both of which are penalized least-squares regressions, have become popular statistical techniques. This article describes that the FWL theorem remains valid for these penalized least-squares regressions. More precisely, we demonstrate that the covariates corresponding to unpenalized regression parameters in these penalized least-squares regression can be projected out. Some other results related to the FWL theorem in such penalized least-squares regressions are also presented.

Suggested Citation

  • Hiroshi Yamada, 2017. "The Frisch–Waugh–Lovell theorem for the lasso and the ridge regression," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(21), pages 10897-10902, November.
    • Handle: RePEc:taf:lstaxx:v:46:y:2017:i:21:p:10897-10902
    DOI: 10.1080/03610926.2016.1252403
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/03610926.2016.1252403
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/03610926.2016.1252403?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. Robert Adamek & Stephan Smeekes & Ines Wilms, 2022. "Local Projection Inference in High Dimensions," Papers 2209.03218, arXiv.org, revised Feb 2023.
    2. Smeekes, Stephan & Wijler, Etienne, 2021. "An automated approach towards sparse single-equation cointegration modelling," Journal of Econometrics, Elsevier, vol. 221(1), pages 247-276.
    3. Ruixue Du & Hiroshi Yamada, 2020. "Principle of Duality in Cubic Smoothing Spline," Mathematics, MDPI, vol. 8(10), pages 1-19, October.

    More about this item

    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:taf:lstaxx:v:46:y:2017:i:21:p:10897-10902. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/lsta .

    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.