Tuning parameter selection in LASSO regression

We propose a new method to select the tuning parameter in lasso regression. Unlike the previous proposals, the method is iterative and thus it is particularly efficient when multiple tuning parameters have to be selected. The method also applies to more general regression frameworks, such as generalized linear models with non-normal responses. Simulation studies show our proposal performs well, and most of times, better when compared with the traditional Bayesian Information Criterion and Cross validation.