GCV {g.ridge}

GCV (generalized cross-validation)

Description

The CGV function gives the sum of cross-validated squared errors that can be used to optimize tuning parameters in ridge regression and generalized ridge regression. See Golub et al. (1979), and Sections 2.3 and 3.3 of Yang and Emura (2017) for details.

Usage

GCV(X, Y, k, W = diag(ncol(X)))

Arguments

X

matrix of explanatory variables (design matrix)

Y

vector of response variables

k

shrinkage parameter (>0); it is the "lambda" parameter

W

matrix of weights (default is the identity matrix)

Value

The value of GCV

References

Yang SP, Emura T (2017) A Bayesian approach with generalized ridge estimation for high-dimensional regression and testing, Commun Stat-Simul 46(8): 6083-105.

Golub GH, Heath M, Wahba G (1979) Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21:215–223.

Examples

n=100 # no. of observations
p=100 # no. of dimensions
q=r=10 # no. of nonzero coefficients
beta=c(rep(0.5,q),rep(0.5,r),rep(0,p-q-r))
X=X.mat(n,p,q,r)
Y=X%*%beta+rnorm(n,0,1)
GCV(X,Y,k=1)