LASSO regression via smooth L1-norm approximation

Abstract

This paper discusses estimation of regression model with LASSO penalty when the L1-norm is replaced with its parametric smooth approximation. The resulting parameter estimators are more manageable than those from standard LASSO, standard errors are easy computed via a sandwich formula, and the model degrees of freedom may be computed straightforwardly. Moreover the resulting objective function may be minimized using usual optimization algorithms for regular models, for instance Newton-Raphson or iterative least squares.