Multi-Response Bridge Regularization Parameter Selection via Multivariate Generalized Information Criterion

Abstract

This paper proposes a multivariate form of generalized information criterion (MGIC) for the multivariate response bridge regression (multi-bridge) model. Also, we prove the identifiability of the multi-bridge as a prerequisite for model selection. We introduce the general form of MGIC for regularization parameter selection in the multi-bridge model. We assess the performance of MGIC variants from three viewpoints: consistency of the obtained models, analysis of high-dimensional data, and comparison to other criteria. Based on the numerical study, we reach better performance for MGIC in comparison to other common criteria (cross-validation and GCV) using simulated and real datasets.