## Bandwidth selection for kernel density estimation.(English)Zbl 0749.62022

From the author’s abstract: The problem of automatic bandwidth selection for a kernel density estimator is considered. Based on characteristic functions, an important expression for the cross-validation bandwidth estimate is obtained. On its basis it is shown that a certain stabilized bandwidth selector gives a strongly consistent estimate of the optimal bandwidth. For sufficiently smooth density functions it is shown that the stabilized bandwidth estimate is asymptotically normal with a relative convergence rate $$n^{-1/2}$$ instead of $$n^{-1/10}$$ for the cross- validation estimate. A plug-in estimate and an adjusted plug-in estimate are proposed and their asymptotic distributions are obtained. Simulation results verify that the proposed procedures perform much better than the cross-validation for finite samples.

### MSC:

 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference 62E20 Asymptotic distribution theory in statistics
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