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，尤其是在高维稀疏场景下。计算机科学领域开发的新型优化方法为鲁棒统计学提供了新机遇。本文探讨如何利用这些方法实现鲁棒稀疏关联估计量。该问题可分解为鲁棒估计步骤与后续解耦（双）凸优化步骤。通过结合增广拉格朗日算法与自适应梯度下降法，引入诱导稀疏性的适当约束。我们提供了算法精度的相关结果，并展示了其相较于现有算法的优势。高维实证案例进一步验证了该方法的实用性，且该框架可推广至其他鲁棒稀疏估计量。