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September, 1987 Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set
Ker-Chau Li
Ann. Statist. 15(3): 958-975 (September, 1987). DOI: 10.1214/aos/1176350486

Abstract

$C_p, C_L$, cross-validation and generalized cross-validation are useful data-driven techniques for selecting a good estimate from a proposed class of linear estimates. The asymptotic behaviors of these procedures are studied. Some easily interpretable conditions are derived to demonstrate the asymptotic optimality. It is argued that cross-validation and generalized cross-validation can be viewed as some special ways of applying $C_L$. Applications in nearest-neighbor nonparametric regression and in model selection are discussed in detail.

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Ker-Chau Li. "Asymptotic Optimality for $C_p, C_L$, Cross-Validation and Generalized Cross-Validation: Discrete Index Set." Ann. Statist. 15 (3) 958 - 975, September, 1987. https://doi.org/10.1214/aos/1176350486

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0653.62037
MathSciNet: MR902239
Digital Object Identifier: 10.1214/aos/1176350486

Subjects:
Primary: 62G99
Secondary: 62J05, 62J07, 62J99

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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