Evaluation of Consistency of Model Selection Criteria in Multivariate Linear Regression Models by Large-sample and High-dimensional Asymptotic Theory under Nonnormality

Abstract

In this paper, we deal with a mdoel selection in multivariate linear regression models, based on minimization of the model selection criterion (MSC) that includes the generalized information criterion (GIC) and the generalized C_p (GC_p) criterion as a special case, when the dimension of the response variables vector may be large but still smaller than the sample size. Recently, the consistent MSC evaluated from the large-sample and high-dimensional asymptotic theory was proposed. The consistency of the MSC proposed in the previous study can be achieved whenever the dimension of the response variables vector is fixed or goes to infinity. Unfortunately, the consistency property was showed under the assumption that the true distribution of response variables is the multivariate normal distribution. In this paper, we show that the MSC proposed in the previous study has consistency under the violation of normality of the true distribution.