The Annals of Statistics

On the Amount of Noise Inherent in Bandwidth Selection for a Kernel Density Estimator

Peter Hall and J. S. Marron

Full-text: Open access

Abstract

In the setting of kernel density estimation, data-driven bandwidth, i.e., smoothing parameter, selectors are considered. It is seen that there is a well-defined, and surprisingly restrictive, bound on the rate of convergence of any automatic bandwidth selection method to the optimum. The method of least squares cross-validation achieves this bound.

Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 163-181.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350259

Digital Object Identifier
doi:10.1214/aos/1176350259

Mathematical Reviews number (MathSciNet)
MR885730

Zentralblatt MATH identifier
0667.62022

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62E20: Asymptotic distribution theory 62H99: None of the above, but in this section

Keywords
Bandwidth cross-validation data-driven estimate noise smoothing parameter selection window width

Citation

Hall, Peter; Marron, J. S. On the Amount of Noise Inherent in Bandwidth Selection for a Kernel Density Estimator. Ann. Statist. 15 (1987), no. 1, 163--181. doi:10.1214/aos/1176350259. https://projecteuclid.org/euclid.aos/1176350259


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