Open Access
December, 1984 An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates
Charles J. Stone
Ann. Statist. 12(4): 1285-1297 (December, 1984). DOI: 10.1214/aos/1176346792


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.


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Charles J. Stone. "An Asymptotically Optimal Window Selection Rule for Kernel Density Estimates." Ann. Statist. 12 (4) 1285 - 1297, December, 1984.


Published: December, 1984
First available in Project Euclid: 12 April 2007

zbMATH: 0599.62052
MathSciNet: MR760688
Digital Object Identifier: 10.1214/aos/1176346792

Primary: 62G99
Secondary: 62H99

Keywords: asymptotic optimality , cross-validation , Kernel density estimate , poissonization , window selection rule

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 4 • December, 1984
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