The Annals of Statistics

An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates

Charles J. Stone

Full-text: Open access

Abstract

Kernel estimates of an unknown multivariate density are investigated, with mild restrictions being placed on the kernel. A window selection rule is considered, which can be interpreted in terms of cross-validation. Under the mild assumption that the unknown density and its one-dimensional marginals are bounded, the rule is shown to be asymptotically optimal. This strengthens recent results of Peter Hall.

Article information

Source
Ann. Statist. Volume 12, Number 4 (1984), 1285-1297.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176346792

Digital Object Identifier
doi:10.1214/aos/1176346792

Mathematical Reviews number (MathSciNet)
MR760688

Zentralblatt MATH identifier
0599.62052

JSTOR
links.jstor.org

Subjects
Primary: 62G99: None of the above, but in this section
Secondary: 62H99: None of the above, but in this section

Keywords
Kernel density estimate window selection rule cross-validation asymptotic optimality Poissonization

Citation

Stone, Charles J. An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates. Ann. Statist. 12 (1984), no. 4, 1285--1297. doi:10.1214/aos/1176346792. http://projecteuclid.org/euclid.aos/1176346792.


Export citation