CVTuningCov (version 1.0)

regular.CV: Select Tuning Parameter for Regularized Covariance Matrix by K-fold CV

Description

Apply K-fold cross-validation (CV) to select tuning parameters for regualrized covariance matrix with banding, tapering, soft-thresholding or hard-thresholding method under the Frobenius norm or the operator norm. Two versions of K-fold CV are applied: 1) the regular one, K-1 folds are used to train and 1 fold is used to validate; 2) the reverse one, 1 fold is used to train and K-1 folds are used to validate.

Usage

regular.CV(X, k.grid = 0.5, method = "Tapering", fold = 5, norm = "F", seed=10323)

Arguments

X

input data matrix with dimension n*p. n indicates the sample size and p indicates the dimension of the corresponding random vector.

k.grid

the default value is 0.5.

method

the regularized method, which can be "Banding", "Tapering", "HardThresholding" or "SoftThresholding". the default value is "Tapering".

fold

the number of folds in K-fold CV. integers only. the default number is 5.

norm

the norms which can be used to measure the estimation accuracy, which can be the Frobenius norm "F" or the operator norm "L2".

seed

the default value is 10323.

Value

• A list including elements:
• CV.k
  a 2-dimensional vector denoting the optimal tuning parameters selected by K-fold CV with its first component as the one from regular version and its second component as the one from the reverse version.
• k.grid
  the vector of tuning parameters
• CV.pre.error
  a matrix with two columns denoting predicting errors by K-fold CV at each element of tuning parameters based on the selected norm with its first column demoting the values from regular version and the second column denoting the values from the reverse version. The number of rows equals the length of the vector for tuning parameters.

Examples

library(MASS);
n <- 50;
p <- 50;
fold <- 3;
k.grid <- seq(0,2*(p-1),by=1);
Sigma <- AR1(p, rho=0.6);
X <- mvrnorm(n,rep(0,p),Sigma);
CV.F.fit <- regular.CV(X,k.grid, method='Tapering',fold=fold,norm='F');
CV.F.fit$CV.k;