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December, 1983 On the Consistency of Cross-Validation in Kernel Nonparametric Regression
Wing Hung Wong
Ann. Statist. 11(4): 1136-1141 (December, 1983). DOI: 10.1214/aos/1176346327

Abstract

For the nonparametric regression model $Y(t_i) = \theta(t_i) + \varepsilon(t_i)$ where $\theta$ is a smooth function to be estimated, $t_i$'s are nonrandom, $\varepsilon(t_i)$'s are i.i.d. errors, this paper studies the behavior of the kernel regression estimate $\hat{\theta}(t) = \big\lbrack \sum^n_{j=1}K \big(\frac{t_j - t}{\lambda}\big) Y(t_j) \big\rbrack / \big\lbrack\ sum^n_{j=1} K \big(\frac{t_j - t}{\lambda}\big) \big\rbrack$ when $\lambda$ is chosen by cross-validation on the average squared error. Strong consistency in terms of the average squared error is established for uniform spacing, compact kernel and finite fourth error moment.

Citation

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Wing Hung Wong. "On the Consistency of Cross-Validation in Kernel Nonparametric Regression." Ann. Statist. 11 (4) 1136 - 1141, December, 1983. https://doi.org/10.1214/aos/1176346327

Information

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

zbMATH: 0539.62046
MathSciNet: MR720259
Digital Object Identifier: 10.1214/aos/1176346327

Subjects:
Primary: 62G05

Rights: Copyright © 1983 Institute of Mathematical Statistics

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Vol.11 • No. 4 • December, 1983
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