The 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 nature.

中文翻译：

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对协变量依赖下变量选择的 LASSO 及其衍生物的批判性评论

当协变量之间存在依赖结构时，测试了众所周知的 LASSO 回归作为变量选择器的局限性。我们分析了n ≥ p的经典情况和p  >  n的高维框架。通过广泛的模拟研究分析和测试了该方法的已知限制特性，以保证最优性，以及实践中的不便。这些缺点的例子展示了利用不同的依赖场景。为了寻求改进，对 LASSO 衍生物和替代品进行了广泛的比较。最后，我们给出了一些指导，说明哪些程序在考虑到的数据性质方面最有效。