Collinear Groupwise Selection via Scaled Group Lasso

This paper addresses model selection and estimation in multiple linear regression models with grouped covariates. We propose a regularization method, called Scaled Group Lasso (SGLASSO), that is designed to account for correlation patterns among groups. The method combines group-wise sparsity with James–Stein-type shrinkage toward a scaled least-squares target, providing a way to balance prediction accuracy, coefficient estimation, and model sparsity under collinearity. We develop a block-wise coordinate descent algorithm integrated with sequential screening and Karush–Kuhn–Tucker checks to enhance computational efficiency. To evaluate its performance, we conduct both low- and high-dimensional simulations, tuning-sensitivity analyses, scalability comparisons, and three real-data applications involving grouped predictors.