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September, 1986 Asymptotic Optimality of $C_L$ and Generalized Cross-Validation in Ridge Regression with Application to Spline Smoothing
Ker-Chau Li
Ann. Statist. 14(3): 1101-1112 (September, 1986). DOI: 10.1214/aos/1176350052

Abstract

The asymptotic optimality of Mallows' $C_L$ and generalized cross-validation is demonstrated in the setting of ridge regression. An application is made to spline smoothing in nonparametric regression. A counterexample is given to help understand why sometimes GCV may not be asymptotically optimal. The coefficient of variation for the eigenvalues of the information matrix must be large in order to guarantee the optimality of GCV. The proff is based on the connection between GCV and Stein's unbiased risk estimate.

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Ker-Chau Li. "Asymptotic Optimality of $C_L$ and Generalized Cross-Validation in Ridge Regression with Application to Spline Smoothing." Ann. Statist. 14 (3) 1101 - 1112, September, 1986. https://doi.org/10.1214/aos/1176350052

Information

Published: September, 1986
First available in Project Euclid: 12 April 2007

zbMATH: 0629.62043
MathSciNet: MR856808
Digital Object Identifier: 10.1214/aos/1176350052

Subjects:
Primary: 62G05
Secondary: 62G99

Rights: Copyright © 1986 Institute of Mathematical Statistics

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Vol.14 • No. 3 • September, 1986
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