lm_ShVAR_KCV {VARshrink}

K-fold Cross Validation for Selection of Shrinkage Parameters of Semiparametric Bayesian Shrinkage Estimator for Multivariate Regression

Description

Estimate regression coefficients and scale matrix for noise by using semiparametric Bayesian shrinkage estimator, whose shrinkage parameters are selected by K-fold cross validation (KCV).

Usage

lm_ShVAR_KCV(Y, X, dof = Inf, lambda = NULL, lambda_var = NULL,
  prior_type = c("NCJ", "CJ"), num_folds = 5, m0 = ncol(Y))

Arguments

Y

An N x K matrix of dependent variables.

X

An N x M matrix of regressors.

dof

Degree of freedom for multivariate t-distribution. If dof = Inf (default), then multivariate normal distribution is applied and weight vector q is not estimated. If dof = NULL or a numeric vector, then dof is selected by K-fold CV automatically and q is estimated.

lambda

If NULL or a vector of length >=2, it is selected by KCV.

lambda_var

If NULL or a vector of length >=2, it is selected by KCV.

prior_type

"NCJ" for non-conjugate prior and "CJ" for conjugate prior for scale matrix Sigma.

num_folds

Number of folds for KCV.

m0

A hyperparameter for inverse Wishart distribution for Sigma

Details

The shrinkage parameters, lambda and lambda_var, for the semiparametric Bayesian shrinkage estimator are selected by KCV. See help(lm_semi_Bayes_PCV) for details about semiparametric Bayesian estimator.

References

N. Lee, H. Choi, and S.-H. Kim (2016). Bayes shrinkage estimation for high-dimensional VAR models with scale mixture of normal distributions for noise. Computational Statistics & Data Analysis 101, 250-276. doi: 10.1016/j.csda.2016.03.007