The Annals of Statistics

Best Possible Constant for Bandwidth Selection

Jianqing Fan and James S. Marron

Full-text: Open access

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 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.

Article information

Source
Ann. Statist., Volume 20, Number 4 (1992), 2057-2070.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348902

Digital Object Identifier
doi:10.1214/aos/1176348902

Mathematical Reviews number (MathSciNet)
MR1193325

Zentralblatt MATH identifier
0765.62041

JSTOR
links.jstor.org

Subjects
Primary: 62G07: Density estimation
Secondary: 62B10: Information-theoretic topics [See also 94A17] 62C20: Minimax procedures

Keywords
Bandwidth selection efficient bounds kernel density estimator semiparametric methods

Citation

Fan, Jianqing; Marron, James S. Best Possible Constant for Bandwidth Selection. Ann. Statist. 20 (1992), no. 4, 2057--2070. doi:10.1214/aos/1176348902. https://projecteuclid.org/euclid.aos/1176348902


Export citation