IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Strongly consistent density estimation of the regression residual

Listed author(s):
  • Györfi, László
  • Walk, Harro
Registered author(s):

    Consider the regression problem with a response variable Y and with a d-dimensional feature vector X. For the regression function m(x)=E{Y|X=x}, this paper investigates methods for estimating the density of the residual Y−m(X) from independent and identically distributed data. For heteroscedastic regression, we prove the strong universal (density-free) L1-consistency of a recursive and a nonrecursive kernel density estimate based on a regression estimate.

    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.

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 11 ()
    Pages: 1923-1929

    in new window

    Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1923-1929
    DOI: 10.1016/j.spl.2012.06.021
    Contact details of provider: Web page:

    Order Information: Postal:

    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.:

    in new window

    1. Kohler, Michael, 1999. "Universally Consistent Regression Function Estimation Using Hierarchial B-Splines," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 138-164, January.
    2. Harro Walk, 2005. "Strong universal consistency of smooth kernel regression estimates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 665-685, December.
    3. Sam Efromovich, 2007. "Optimal nonparametric estimation of the density of regression errors with finite support," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 617-654, December.
    4. Devroye, Luc & Felber, Tina & Kohler, Michael & Krzyżak, Adam, 2012. "L1-consistent estimation of the density of residuals in random design regression models," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 173-179.
    5. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    6. Ahmad, Ibrahim A., 1992. "Residuals density estimation in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 133-139, May.
    7. Michael G. Akritas, 2001. "Non-parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567.
    8. Györfi L. & Kohler M. & Walk H., 1998. "Weak And Strong Universal Consistency Of Semi-Recursive Kernel And Partitioning Regression Estimates," Statistics & Risk Modeling, De Gruyter, vol. 16(1), pages 1-18, January.
    9. 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.
    10. Cheng, Fuxia, 2002. "Consistency of error density and distribution function estimators in nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 257-270, October.
    11. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2009. "Estimating the error distribution function in nonparametric regression with multivariate covariates," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 957-964, April.
    12. Müller Ursula U. & Schick Anton & Wefelmeyer Wolfgang, 2007. "Estimating the error distribution function in semiparametric regression," Statistics & Risk Modeling, De Gruyter, vol. 25(1/2007), pages 1-18, January.
    Full references (including those not matched with items on IDEAS)

    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:eee:stapro:v:82:y:2012:i:11:p:1923-1929. 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: (Dana Niculescu)

    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.