Abstarct: In regression analysis if the number of explanalory variables is lange. estimation of parameters with least squares method is not relevant and one must use penalized estimators. On of the most efficient penalized estimators is the LASSO. This estimator is not differentiable at zero and hence not normally distributed. In this dissertation we study the performance of a differentiable LASSO which has asymptotic normal distribution. whit some simutation studies and real data analyses, we evaluate the performanc of this estimator along with a difference-baxsed differentiable LASSO.