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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 - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - CNRS - Centre National de la Recherche Scientifique - ECM - Ecole Centrale de Marseille)

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
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    Keywords

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

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