Maronna's and Tyler's $M$-estimators are among the most widely used robust estimators for scatter matrices. However, when the dimension of observations is relatively high, their performance can substantially deteriorate in certain situations, particularly in the presence of clustered outliers. To address this issue, we propose an estimator that shrinks the estimated precision matrix toward the identity matrix. We derive a sufficient condition for its existence, discuss its statistical interpretation, and establish upper and lower bounds for its breakdown point. Numerical experiments confirm robustness of the proposed method.

翻译：Maronna和Tyler的$M$估计是散点矩阵最广泛使用的稳健估计方法之一。然而，当观测维度较高时，其性能在某些情况下会显著下降，尤其是在存在聚类异常值的情况下。为解决这一问题，我们提出一种将估计的精度矩阵向单位矩阵收缩的估计方法。我们推导了其存在的充分条件，讨论了其统计解释，并建立了其崩溃点的上下界。数值实验证实了所提方法的稳健性。