SCAD regression model selection with information criteria for multivariate response models

This paper provides an objective function for smoothly clipped absolute deviation (SCAD) regression models with multivariate responses. The log-likelihood of a multivariate normal distribution is considered instead of $L_2$ norm to create the model's objective function. Additionally, the SCAD penalty has a tuning parameter, and the information criteria, suitable for the proposed model are presented to select the tuning parameter. Based on numerical studies, the consistency of the proposed information criteria is checked via simulation experiments. Moreover, the best criterion is introduced using simulated and real datasets.