A Consistent Likelihood-Based Variable Selection Method in Normal Multivariate Linear Regression

We propose a likelihood-based variable selection method for selecting explanatory variables in normality-assumed multivariate linear regression contexts. The proposed method is reasonably fast in terms of run-time, and it has a selection consistency when the sample size always tends to infinity, but the number of response and explanatory variables does not necessarily have to tend to infinity. It can be expected that the probability of selecting the true subset by the proposed method is high under a moderate sample size.