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, structures are considered as (1) independent structure same variance, (2) different variances, and (3) uniform structure. A sufficient condition model selection consistency is obtained using a method under asymptotic framework, such that sample size n, number p variables, k explanatory large, p/n→c1∈(0,1) k/n→c2∈[0,1), where c1+c2<1.