论文标题
图形套索估计器的影响函数
The Influence Function of Graphical Lasso Estimators
论文作者
论文摘要
一组变量之间编码条件线性依赖关系的精确矩阵构成了多变量分析中感兴趣的重要对象。精确矩阵（例如图形套索（Glasso））的稀疏估计程序在促进可解释性的过程中获得了流行，从而将有条件地依赖的变量对分开，这些变量与独立的变量（给定所有其他变量）。然而，格拉多缺乏对异常值的鲁棒性。为了克服这个问题，通常会采用强大的插件程序，从而从强大的协方差估计中而不是样品协方差计算玻璃，从而提供了防止异常值的保护。在本文中，我们从理论上研究了此类估计值，通过得出和比较其影响功能，灵敏度曲线和渐近方差。
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.
