A Permutation Approach for Selecting the Penalty Parameter in Penalized Model Selection

We describe a simple, computationally efficient, permutation-based procedure for selecting the penalty parameter in LASSO-penalized regression. The procedure, permutation selection, is intended for applications where variable selection is the primary focus, and can be applied in a variety of structural settings, including that of generalized linear models. We briefly discuss connections between permutation selection and existing theory for the LASSO. In addition, we present a simulation study and an analysis of real biomedical data sets in which permutation selection is compared with selection based on the following: cross-validation (CV), the Bayesian information criterion (BIC), scaled sparse linear regression, and a selection method based on recently developed testing procedures for the LASSO.