Although robust statistical estimators are less affected by outlying observations, their computation is usually more challenging. This is particularly the case in high-dimensional sparse settings. The availability of new optimization procedures, mainly developed in the computer science domain, offers new possibilities for the field of robust statistics. This paper investigates how such procedures can be used for robust sparse association estimators. The problem can be split into a robust estimation step followed by an optimization for the remaining decoupled, (bi-)convex problem. A combination of the augmented Lagrangian algorithm and adaptive gradient descent is implemented to also include suitable constraints for inducing sparsity. We provide results concerning the precision of the algorithm and show the advantages over existing algorithms in this context. High-dimensional empirical examples underline the usefulness of this procedure. Extensions to other robust sparse estimators are possible.

翻译：尽管鲁棒统计估计量受异常值影响较小，但其计算通常更具挑战性，尤其是在高维稀疏设置中。计算机科学领域主要开发的新型优化过程为鲁棒统计领域提供了新的可能性。本文探讨了如何将这些过程应用于鲁棒稀疏关联估计量。该问题可分解为一个鲁棒估计步骤，随后对剩余的解耦（双）凸问题进行优化。通过结合增广拉格朗日算法与自适应梯度下降法，引入适当的约束条件以诱导稀疏性。我们提供了关于算法精度的结果，并展示了在此背景下相较于现有算法的优势。高维经验示例突出了该过程的有效性。该方法可推广至其他鲁棒稀疏估计量。