Moderately clipped LASSO

The least absolute shrinkage and selection operator (LASSO) has been widely used in high-dimensional linear regression models. However, it is known that the LASSO selects too many noisy variables. In this paper, we propose a new estimator, the moderately clipped LASSO (MCL), that deletes noisy variables successively without sacrificing prediction accuracy much. Various numerical studies are done to illustrate superiority of the MCL over other competitors.