IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/halshs-00472750.html
   My bibliography  Save this paper

Explicit Solutions For The Asymptotically-Optimal Bandwidth In Cross Validation

Author

Listed:
  • Karim Abadir

    (Imperial College London)

  • Michel Lubrano

    () (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

Abstract

Least squares cross-validation (CV) methods are often used for automated bandwidth selection. We show that they share a common structure which has an explicit asymptotic solution. Using the framework of density estimation, we consider unbiased, biased, and smoothed CV methods. We show that, with a Student t(nu) kernel which includes the Gaussian as a special case, the CV criterion becomes asymptotically equivalent to a simple polynomial. This leads to optimal-bandwidth solutions that dominate the usual CV methods, definitely in terms of simplicity and speed of calculation, but also often in terms of integrated squared error because of the robustness of our asymptotic solution. We present simulations to illustrate these features and to give practical guidance on the choice of nu.

Suggested Citation

  • Karim Abadir & Michel Lubrano, 2010. "Explicit Solutions For The Asymptotically-Optimal Bandwidth In Cross Validation," Working Papers halshs-00472750, HAL.
  • Handle: RePEc:hal:wpaper:halshs-00472750
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00472750
    as

    Download full text from publisher

    File URL: https://halshs.archives-ouvertes.fr/halshs-00472750/document
    Download Restriction: no

    Other versions of this item:

    More about this item

    Keywords

    bandwidth choice; cross validation; nonparametric density es- timation; analytical solution;

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:hal:wpaper:halshs-00472750. 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: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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 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.

    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.