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March, 1983 Consistent Cross-Validated Density Estimation
Y.-S. Chow, S. Geman, L.-D. Wu
Ann. Statist. 11(1): 25-38 (March, 1983). DOI: 10.1214/aos/1176346053


Application of nonparametric density estimators generally requires the specification of a "smoothing parameter." The kernel estimator, for example, is not fully defined until a window width, or scaling, for the kernels has been chosen. Many "data-driven" techniques have been suggested for the practical choice of smoothing parameter. Of these, the most widely studied is the method of cross-validation. Our own simulations, as well as those of many other investigators, indicate that cross-validated smoothing can be an extremely effective practical solution. However, many of the most basic properties of cross-validated estimators are unknown. Indeed, recent results show that cross-validated estimators can fail even to be consistent for seemingly well-behaved problems. In this paper we will review the application of cross-validation to the smoothing problem, and establish $L_1$ consistency for certain cross-validated kernels and histograms.


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Y.-S. Chow. S. Geman. L.-D. Wu. "Consistent Cross-Validated Density Estimation." Ann. Statist. 11 (1) 25 - 38, March, 1983.


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

zbMATH: 0509.62033
MathSciNet: MR684860
Digital Object Identifier: 10.1214/aos/1176346053

Primary: 62G05
Secondary: 62A10

Keywords: consistency , cross-validation , Nonparametric density estimation

Rights: Copyright © 1983 Institute of Mathematical Statistics


Vol.11 • No. 1 • March, 1983
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