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December, 1992 Best Possible Constant for Bandwidth Selection
Jianqing Fan, James S. Marron
Ann. Statist. 20(4): 2057-2070 (December, 1992). DOI: 10.1214/aos/1176348902


For the data based choice of the bandwidth of a kernel density estimator, several methods have recently been proposed which have a very fast asymptotic rate of convergence to the optimal bandwidth. In particular the relative rate of convergence is the square root of the sample size, which is known to be the best possible. The point of this paper is to show how semiparametric arguments can be employed to calculate the best possible constant coefficient, that is, an analog of the usual Fisher information, in this convergence. This establishes an important benchmark as to how well bandwidth selection methods can ever hope to perform. It is seen that some existing methods attain the bound, others do not.


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Jianqing Fan. James S. Marron. "Best Possible Constant for Bandwidth Selection." Ann. Statist. 20 (4) 2057 - 2070, December, 1992.


Published: December, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0765.62041
MathSciNet: MR1193325
Digital Object Identifier: 10.1214/aos/1176348902

Primary: 62G07
Secondary: 62B10, 62C20

Rights: Copyright © 1992 Institute of Mathematical Statistics


Vol.20 • No. 4 • December, 1992
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