A note on kernel density estimation at a parametric rate

Author: Chacón J. E.   Montanero J.   Nogales A. G.  

Publisher: Taylor & Francis Ltd

ISSN: 1048-5252

Source: Journal of Nonparametric Statistics, Vol.19, Iss.1, 2007-01, pp. : 13-21

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Abstract

In the context of kernel density estimation, we give a characterization of the kernels for which the parametric mean integrated squared error (MISE) rate n-1 may be obtained, where n is the sample size. Also, for the cases where this rate is attainable, we give an asymptotic bandwidth choice that makes the kernel estimator consistent in mean integrated squared error at that rate and a numerical example showing the superior performance of the superkernel estimator when the bandwidth is properly chosen.