High-Dimensional Consistencies of KOO Methods for the Selection of Variables in Multivariate Linear Regression Models with Covariance Structures

In this paper, we consider the high-dimensional consistencies of KOO methods for selecting response variables in multivariate linear regression with covariance structures. Here, the covariance structures are considered as (1) independent covariance structure with the same variance, (2) independent covariance structure with different variances, and (3) uniform covariance structure. A sufficient condition for model selection consistency is obtained using a KOO method under a high-dimensional asymptotic framework, such that sample size n, the number p of response variables, and the number k of explanatory variables are large, as in p/n -> c(1) is an element of (0,1) and k/n-* c(2 )is an element of [0, 1), where c(1 )+ c(2 )< 1.