Advanced Search
MyIDEAS: Login to save this article or follow this journal

Universally Consistent Regression Function Estimation Using Hierarchial B-Splines


Author Info

  • Kohler, Michael
Registered author(s):


    Estimation of multivariate regression functions from i.i.d. data is considered. We construct estimates by empiricalL2-error minimization over data-dependent spaces of polynomial spline functions. For univariate regression function estimation these spaces are spline spaces with data-dependent knot sequences. In the multivariate case, we use so-called hierarchical spline spaces which are defined as linear span of tensor product B-splines with nested knot sequences. The knot sequences of the chosen B-splines depend locally on the data. Â We show the strongL2-consistency of the estimators without any condition on the underlying distribution. The estimators are similar to histogram regression estimators using data-dependent partitions and partitioning regression estimators based on local polynomial fits. The main difference is that the estimators considered here are smooth functions, which seems to be desirable especially in the case that the regression function to be estimated is smooth.

    Download Info

    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:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 68 (1999)
    Issue (Month): 1 (January)
    Pages: 138-164

    as in new window
    Handle: RePEc:eee:jmvana:v:68:y:1999:i:1:p:138-164

    Contact details of provider:
    Web page:

    Order Information:

    Related research

    Keywords: data-dependent partitions integrated squared error least squares estimate polynomial splines regression estimate universal consistency;


    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Györfi, László & Walk, Harro, 1997. "On the strong universal consistency of a recursive regression estimate by Pál Révész," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 177-183, January.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:
    1. Kohler, Michael & Máthé, Kinga & Pintér, Márta, 2002. "Prediction from Randomly Right Censored Data," Journal of Multivariate Analysis, Elsevier, vol. 80(1), pages 73-100, January.
    2. Györfi, László & Walk, Harro, 2012. "Strongly consistent density estimation of the regression residual," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1923-1929.
    3. Kohler, Michael & Krzyzak, Adam & Walk, Harro, 2006. "Rates of convergence for partitioning and nearest neighbor regression estimates with unbounded data," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 311-323, February.


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


    Access and download statistics


    When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:68:y:1999:i:1:p:138-164. 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: (Zhang, Lei).

    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.