On model selection consistency using a kick-one-out method for selecting response variables in high-dimensional multivariate linear regression

This article deals with the selection of non redundant response variables in normality-assumed multivariate linear regression, where the redundancy of the response variables is defined by conditional expectation. A sufficient condition for model selection consistency is obtained using a kick-one-out method based on the generalized information criterion under a high-dimensional asymptotic framework such that the sample size tends to infinity and the number of response variables and explanatory variables does not exceed the sample size but may tend to infinity. A consistent kick-one-out method using the obtained condition is proposed. Simulation results show that the proposed method has a high probability of selecting true, non redundant variables.