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Explicit Solutions for the Asymptotically-Optimal Bandwidth in Cross Validation

Author

Listed:
  • Karim M. Abadir

    () (Imperial College, London, UK)

  • Michel Lubrano

    () (Greqam-Cnrs, Centre de la Vieille Charité, Marseille, France)

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 that we derive. Using the framework of density estimation, we consider unbiased, biased, and smoothed CV methods. We show that, with a Student t(v) 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, hence also alleviating the notorious sample variability of CV. We present simulations to illustrate these features and to give practical guidance on the choice of v.

Suggested Citation

  • Karim M. Abadir & Michel Lubrano, 2010. "Explicit Solutions for the Asymptotically-Optimal Bandwidth in Cross Validation," Working Paper series 16_10, Rimini Centre for Economic Analysis.
  • Handle: RePEc:rim:rimwps:16_10
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    Keywords

    bandwidth choice; cross validation; nonparametric density estimation; analytical solution;

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