The precision matrix that encodes conditional linear dependency relations among a set of variables forms an important object of interest in multivariate analysis. Sparse estimation procedures for precision matrices such as the graphical lasso (Glasso) gained popularity as they facilitate interpretability, thereby separating pairs of variables that are conditionally dependent from those that are independent (given all other variables). Glasso lacks, however, robustness to outliers. To overcome this problem, one typically applies a robust plug-in procedure where the Glasso is computed from a robust covariance estimate instead of the sample covariance, thereby providing protection against outliers. In this paper, we study such estimators theoretically, by deriving and comparing their influence function, sensitivity curves and asymptotic variances.

翻译：编码一组变量间条件线性依赖关系的精度矩阵是多变量分析中的重要研究对象。精度矩阵的稀疏估计方法（如图形套索，Glasso）因能促进可解释性而广受欢迎——该方法将条件依赖的变量对与条件独立的变量对（给定其他所有变量条件下）加以区分。然而，Glasso缺乏对异常值的鲁棒性。为解决此问题，通常采用稳健插件法：基于稳健协方差估计（而非样本协方差）计算Glasso，从而提供抗异常值保护。本文从理论上研究此类估计量，通过推导并比较其影响函数、敏感度曲线及渐近方差展开分析。