The Annals of Statistics

Large Sample Optimality of Least Squares Cross-Validation in Density Estimation

Peter Hall

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 11, Number 4 (1983), 1156-1174.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346329

Digital Object Identifier
doi:10.1214/aos/1176346329

Mathematical Reviews number (MathSciNet)
MR720261

Zentralblatt MATH identifier
0599.62051

JSTOR
links.jstor.org

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

Keywords
Asymptotically optimal Bowman and Rudemo's method cross-validation integrated square error least squares nonparametric density estimation

Citation

Hall, Peter. Large Sample Optimality of Least Squares Cross-Validation in Density Estimation. Ann. Statist. 11 (1983), no. 4, 1156--1174. doi:10.1214/aos/1176346329. https://projecteuclid.org/euclid.aos/1176346329


Export citation