IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v62y2000i2p413-428.html
   My bibliography  Save this article

Modelling and smoothing parameter estimation with multiple quadratic penalties

Author

Listed:
  • S. N. Wood

Abstract

Penalized likelihood methods provide a range of practical modelling tools, including spline smoothing, generalized additive models and variants of ridge regression. Selecting the correct weights for penalties is a critical part of using these methods and in the single‐penalty case the analyst has several well‐founded techniques to choose from. However, many modelling problems suggest a formulation employing multiple penalties, and here general methodology is lacking. A wide family of models with multiple penalties can be fitted to data by iterative solution of the generalized ridge regression problem minimize ||W1/2 (Xp−y) ||2ρ+Σi=1m θip′Sip (p is a parameter vector, X a design matrix, Si a non‐negative definite coefficient matrix defining the ith penalty with associated smoothing parameter θi, W a diagonal weight matrix, y a vector of data or pseudodata and ρ an ‘overall’ smoothing parameter included for computational efficiency). This paper shows how smoothing parameter selection can be performed efficiently by applying generalized cross‐validation to this problem and how this allows non‐linear, generalized linear and linear models to be fitted using multiple penalties, substantially increasing the scope of penalized modelling methods. Examples of non‐linear modelling, generalized additive modelling and anisotropic smoothing are given.

Suggested Citation

  • S. N. Wood, 2000. "Modelling and smoothing parameter estimation with multiple quadratic penalties," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 413-428.
  • Handle: RePEc:bla:jorssb:v:62:y:2000:i:2:p:413-428
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00240
    Download Restriction: no

    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:bla:jorssb:v:62:y:2000:i:2:p:413-428. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: http://edirc.repec.org/data/rssssea.html .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.