Asymptotic Optimality of $C_L$ and Generalized Cross-Validation in Ridge Regression with Application to Spline Smoothing
The Annals of StatisticsPublished 1 September 1986Open access
Ker-Chau Li
Citations224
SJR quartileQ1
SJR score4.77
SNIP3.13
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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.
Keywords
Mathematics
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