Explicit Solutions For The Asymptotically-Optimal Bandwidth In Cross Validation
AbstractLeast 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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Date of creation: 13 Apr 2010
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bandwidth choice; cross validation; nonparametric density es- timation; analytical solution;
Other versions of this item:
- Karim M. Abadir & Michel Lubrano, 2010. "Explicit Solutions for the Asymptotically-Optimal Bandwidth in Cross Validation," Working Paper Series 16_10, The Rimini Centre for Economic Analysis.
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