IDEAS home Printed from https://ideas.repec.org/a/bla/jorssb/v60y1998i2p365-375.html
   My bibliography  Save this article

Estimating smooth monotone functions

Author

Listed:
  • J. O. Ramsay

Abstract

Many situations call for a smooth strictly monotone function f of arbitrary flexibility. The family of functions defined by the differential equation D 2f =w Df, where w is an unconstrained coefficient function comprises the strictly monotone twice differentiable functions. The solution to this equation is f = C0 + C1 D−1{exp(D−1w)}, where C0 and C1 are arbitrary constants and D−1 is the partial integration operator. A basis for expanding w is suggested that permits explicit integration in the expression of f. In fitting data, it is also useful to regularize f by penalizing the integral of w2 since this is a measure of the relative curvature in f. Applications are discussed to monotone nonparametric regression, to the transformation of the dependent variable in non‐linear regression and to density estimation.

Suggested Citation

  • J. O. Ramsay, 1998. "Estimating smooth monotone functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 365-375.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:2:p:365-375
    DOI: 10.1111/1467-9868.00130
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9868.00130
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9868.00130?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
    ---><---

    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:60:y:1998:i:2:p:365-375. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .

    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.