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December, 1983 Large Sample Optimality of Least Squares Cross-Validation in Density Estimation
Peter Hall
Ann. Statist. 11(4): 1156-1174 (December, 1983). DOI: 10.1214/aos/1176346329

Abstract

We prove that the method of cross-validation suggested by A. W. Bowman and M. Rudemo achieves its goal of minimising integrated square error, in an asymptotic sense. The tail conditions we impose are only slightly more severe than the hypothesis of finite variance, and so least squares cross-validation does not exhibit the pathological behaviour which has been observed for Kullback-Leibler cross-validation. This is apparently the first time that a cross-validatory procedure for density estimation has been shown to be asymptotically optimal, rather then simply consistent.

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Peter Hall. "Large Sample Optimality of Least Squares Cross-Validation in Density Estimation." Ann. Statist. 11 (4) 1156 - 1174, December, 1983. https://doi.org/10.1214/aos/1176346329

Information

Published: December, 1983
First available in Project Euclid: 12 April 2007

zbMATH: 0599.62051
MathSciNet: MR720261
Digital Object Identifier: 10.1214/aos/1176346329

Subjects:
Primary: 62G05
Secondary: 62E20

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 4 • December, 1983
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