Freijeiro-González, LauraFebrero Bande, ManuelGonzález Manteiga, Wenceslao2022-08-172022-08-172022International Statistical Review (2022), 90, 1, 118–145. https://doi.org/10.1111/insr.12469http://hdl.handle.net/10347/29076The limitations of the well-known LASSO regression as a variable selector are tested when there exists dependence structures among covariates. We analyse both the classic situation with n ≥ p and the high dimensional framework with p > n. Known restrictive properties of this methodology to guarantee optimality, as well as inconveniences in practice, are analysed and tested by means of an extensive simulation study. Examples of these drawbacks are showed making use of different dependence scenarios. In order to search for improvements, a broad comparison with LASSO derivatives and alternatives is carried out. Eventually, we give some guidance about what procedures work best in terms of the considered data natureeng© 2021 The Authors. International Statistical Review published by John Wiley & Sons Ltd on behalf of International Statistical Institute. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are madehttp://creativecommons.org/licenses/by-nc-nd/4.0/Covariates selectionp > nL1 regularisation techniquesLASSOjournal article10.1111/insr.124691751-5823open access