IDEAS home Printed from
   My bibliography  Save this article

Likelihood-Based Local Polynomial Fitting for Single-Index Models


  • Huh, J.
  • Park, B. U.


The parametric generalized linear model assumes that the conditional distribution of a response Y given a d-dimensional covariate X belongs to an exponential family and that a known transformation of the regression function is linear in X. In this paper we relax the latter assumption by considering a nonparametric function of the linear combination [beta]TX, say [eta]0([beta]TX). To estimate the coefficient vector [beta] and the nonparametric component [eta]0 we consider local polynomial fits based on kernel weighted conditional likelihoods. We then obtain an estimator of the regression function by simply replacing [beta] and [eta]0 in [eta]0([beta]TX) by these estimators. We derive the asymptotic distributions of these estimators and give the results of some numerical experiments.

Suggested Citation

  • Huh, J. & Park, B. U., 2002. "Likelihood-Based Local Polynomial Fitting for Single-Index Models," Journal of Multivariate Analysis, Elsevier, vol. 80(2), pages 302-321, February.
  • Handle: RePEc:eee:jmvana:v:80:y:2002:i:2:p:302-321

    Download full text from publisher

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    1. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    2. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
    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.

    Cited by:

    1. Feng, Long & Zou, Changliang & Wang, Zhaojun, 2012. "Rank-based inference for the single-index model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 535-541.
    2. Park, Cheolwoo & Huh, Jib, 2013. "Statistical inference and visualization in scale-space using local likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 336-348.
    3. Huh, Jib, 2010. "Detection of a change point based on local-likelihood," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1681-1700, August.
    4. Huh, Jib, 2012. "Nonparametric estimation of the regression function having a change point in generalized linear models," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 843-851.


    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:eee:jmvana:v:80:y:2002:i:2:p:302-321. 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). General contact details of provider: .

    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 CitEc recognized a reference but did not link an item in RePEc 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 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.