The Annals of Statistics

A Comparison of Cross-Validation Techniques in Density Estimation

J. S. Marron

Full-text: Open access

Abstract

In the setting of nonparametric multivariate density estimation, theorems are established which allow a comparison of the Kullback-Leibler and the least-squares cross-validation methods of smoothing parameter selection. The family of delta sequence estimators (including kernel, orthogonal series, histogram and histospline estimators) is considered. These theorems also show that either type of cross validation can be used to compare different estimators (e.g., kernel versus orthogonal series).

Article information

Source
Ann. Statist., Volume 15, Number 1 (1987), 152-162.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350258

Digital Object Identifier
doi:10.1214/aos/1176350258

Mathematical Reviews number (MathSciNet)
MR885729

Zentralblatt MATH identifier
0619.62032

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G20: Asymptotic properties

Keywords
Cross validation smoothing parameter selection choice of nonparametric estimators bandwidth selection

Citation

Marron, J. S. A Comparison of Cross-Validation Techniques in Density Estimation. Ann. Statist. 15 (1987), no. 1, 152--162. doi:10.1214/aos/1176350258. https://projecteuclid.org/euclid.aos/1176350258


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