The Annals of Statistics

Asymptotic Optimality of $C_L$ and Generalized Cross-Validation in Ridge Regression with Application to Spline Smoothing

Ker-Chau Li

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 14, Number 3 (1986), 1101-1112.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350052

Digital Object Identifier
doi:10.1214/aos/1176350052

Mathematical Reviews number (MathSciNet)
MR856808

Zentralblatt MATH identifier
0629.62043

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62G99: None of the above, but in this section

Keywords
$C_L$ generalized cross-validation ridge regression smoothing splines Stein estimates Stein's unbiased risk estimates

Citation

Li, Ker-Chau. Asymptotic Optimality of $C_L$ and Generalized Cross-Validation in Ridge Regression with Application to Spline Smoothing. Ann. Statist. 14 (1986), no. 3, 1101--1112. doi:10.1214/aos/1176350052. https://projecteuclid.org/euclid.aos/1176350052


Export citation