IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Breaking the Curse of Dimensionality

  • Coppejans, Mark
Registered author(s):

    This paper proposes a new nonparametric estimator for general regression functions with multiple regressors. The method used here is motivated by a remarkable result derived by Kolmogorov (1957) and later tightened by Lorentz (1966). In short, they show that any continuous function of multiple variables can be written as univariate functions. As it stands, this representation is difficult to estimate because of its lack of smoothness. Hence we propose to use a generalization of their representation that allows for the univariate functions to be differentiable. The model will be estimated using B-splines, which have excellent numerical properties. A crucial restriction in this representation is that some of the functions must be increasing. One of the main contributions of this paper is that we develop a method for imposing monotonicity on the cubic B-splines, a priori, such that the estimator is dense in the set of all monotonic cubic B-splines. A simulation experiment shows that the estimator works well when optimization is performed by using the back-fitting algorithm. The monotonic restriction has many other applications besides the one presented here, such as estimating a demand function. With only r + 2 more constraints, it is also possible to impose concavity.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL: http://www.econ.duke.edu/Papers/Abstracts00/abstract.00.13.html
    File Function: main text
    Download Restriction: no

    Paper provided by Duke University, Department of Economics in its series Working Papers with number 00-13.

    as
    in new window

    Length:
    Date of creation: 2000
    Date of revision:
    Handle: RePEc:duk:dukeec:00-13
    Contact details of provider: Postal: Department of Economics Duke University 213 Social Sciences Building Box 90097 Durham, NC 27708-0097
    Phone: (919) 660-1800
    Fax: (919) 684-8974
    Web page: http://econ.duke.edu/

    No references listed on IDEAS
    You can help add them by filling out this form.

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:duk:dukeec:00-13. 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: (Department of Economics Webmaster)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 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.

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.