Best possible constant for bandwidth selection

Jianqing Fan James S Marron

Statistics Theory and Methods mathscidoc:1912.43326

The Annals of Statistics, 2057-2070, 1992.12
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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  title={Best possible constant for bandwidth selection},
  author={Jianqing Fan, and James S Marron},
  booktitle={The Annals of Statistics},
Jianqing Fan, and James S Marron. Best possible constant for bandwidth selection. 1992. In The Annals of Statistics. pp.2057-2070.
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