The Annals of Statistics

Choice of Kernel Order in Density Estimation

Peter Hall and J. S. Marron

Full-text: Open access

Abstract

The selection of the order, i.e., number of vanishing moments, of the kernel in a kernel density estimator is considered from two points of view. First, theoretical properties are investigated by a mean integrated squared error analysis of the problem. Second, and perhaps more importantly, cross validation is proposed as a practical method of choice, and theoretical backing for this is provided through an asymptotic optimality result.

Article information

Source
Ann. Statist., Volume 16, Number 1 (1988), 161-173.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350697

Digital Object Identifier
doi:10.1214/aos/1176350697

Mathematical Reviews number (MathSciNet)
MR924863

Zentralblatt MATH identifier
0637.62035

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62E20: Asymptotic distribution theory

Keywords
Cross validation nonparametric density estimation smoothness variable-order kernel

Citation

Hall, Peter; Marron, J. S. Choice of Kernel Order in Density Estimation. Ann. Statist. 16 (1988), no. 1, 161--173. doi:10.1214/aos/1176350697. https://projecteuclid.org/euclid.aos/1176350697


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