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Explicit Solutions For The Asymptotically-Optimal Bandwidth In Cross Validation

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Author Info

  • Karim Abadir

    (Imperial College London - Imperial College London)

  • Michel Lubrano

    ()
    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - Université de la Méditerranée - Aix-Marseille II - Université Paul Cézanne - Aix-Marseille III - Ecole des Hautes Etudes en Sciences Sociales (EHESS) - CNRS : UMR6579)

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.

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Bibliographic Info

Paper provided by HAL in its series Working Papers with number halshs-00472750.

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Date of creation: 13 Apr 2010
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Handle: RePEc:hal:wpaper:halshs-00472750

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Related research

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

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