DMCA
Best Possible Constant for Bandwidth Selection (1992)
| Venue: | Annals of Statistics, 20, Annals of Statistics |
| Citations: | 11 - 2 self |
BibTeX
@ARTICLE{Fan92bestpossible,
author = {Jianqing Fan and James S. Marron},
title = {Best Possible Constant for Bandwidth Selection},
journal = {Annals of Statistics, 20, Annals of Statistics},
year = {1992}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
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 the particular the relative rate of convergence is the square root of the sample size, which is known to be the possible. The point of this paper is to show how semiparametric arguments can be employed to calculate the best possible constant coefficient, i.e. 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 methods attain the bound, others do not.
