Estimate regression coefficients and scale matrix for noise by using Gibbs MCMC algorithm. The function assumes 1) multivariate t-distribution for noise as a sampling distribution, and 2) noninformative priors for regression coefficients and scale matrix for noise.
lm_full_Bayes_SR(Y, X, dof = Inf, burnincycle = 1000, mcmccycle = 2000)A list object with estimated parameters: Psi, Sigma, dof, delta (delta is the reciprocal of lambda), and lambda. Additional components are se.param (standard error of the parameters) and LINEXVARmodel (estimates under LINEX loss).
An N x K matrix of dependent variables.
An N x M matrix of regressors.
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
dof <= 0, then dof and q are estimated automatically.
If dof is a positive number, q is estimated.
Number of burnin cycles is the number of initially generated sample values to drop. Number of MCMC cycles is the number of generated sample values to compute estimates.
Consider the multivariate regression: $$Y = X \Psi + e, \quad e \sim MVT(0, \nu, \Sigma).$$ \(\Psi\) is a M-by-K matrix of regression coefficients and \(\Sigma\) is a K-by-K scale matrix for multivariate t-distribution for noise.
Sampling distribution for noise e is multivariate t-distribution with degree of freedom dof and scale matrix \(\Sigma: e \sim MVT(0, \nu, \Sigma)\). The priors are noninformative priors: 1) the shrinkage prior for regression coefficients \(\Psi\), and 2) the reference prior for scale matrix \(\Sigma\).
The function implements Gibbs MCMC algorithm for estimating regression coefficients Psi and scale matrix Sigma.
S. Ni and D. Sun (2005). Bayesian estimates for vector autoregressive models. Journal of Business & Economic Statistics 23(1), 105-117.