porridge (version 0.3.3)

ridgePgen.kCV: K-fold cross-validated loglikelihood of ridge precision estimator.

Description

Function that calculates of the k-fold cross-validated negative (!) loglikelihood of the generalized ridge precision estimator.

Usage

ridgePgen.kCV(lambda, Y, fold=nrow(Y), target, 
              nInit=100, minSuccDiff=10^(-5))

Value

The function returns a numeric containing the cross-validated negative loglikelihood.

Arguments

lambda

A symmetric matrix with element-wise positive penalty parameters.

Y

Data matrix with samples as rows and variates as columns.

fold

A numeric or integer specifying the number of folds to apply in the cross-validation.

target

A semi-positive definite target matrix towards which the estimate is shrunken.

nInit

A numeric specifying the number of iterations.

minSuccDiff

A numeric: minimum successive difference (in terms of their penalized loglikelihood) between two succesive estimates to be achieved.

Author

W.N. van Wieringen.

References

van Wieringen, W.N. (2019), "The generalized ridge estimator of the inverse covariance matrix", Journal of Computational and Graphical Statistics, 28(4), 932-942.

See Also

ridgePgen

Examples

# set dimension and sample size
p <- 10
n <- 10

# penalty parameter matrix
lambda       <- matrix(1, p, p)
diag(lambda) <- 0.1

# generate precision matrix
Omega       <- matrix(0.4, p, p)
diag(Omega) <- 1
Sigma       <- solve(Omega)

# data 
Y <- mvtnorm::rmvnorm(n, mean=rep(0,p), sigma=Sigma)
S <- cov(Y)

# find optimal penalty parameters through cross-validation
lambdaOpt <- optPenaltyPgen.kCVauto.banded(Y, 10^(-10), 10^(10), 
                          target=matrix(0, p, p),
                          penalize.diag=FALSE, nInit=100, 
                          minSuccDiff=10^(-5)) 

# format the penalty matrix
lambdaOptMat <- matrix(NA, p, p)
for (j1 in 1:p){
    for (j2 in 1:p){
        lambdaOptMat[j1, j2] <- lambdaOpt * (abs(j1-j2)+1)
    }
}

# generalized ridge precision estimate
Phat <- ridgePgen(S, lambdaOptMat, matrix(0, p, p))