High dimensionality has been a significant feature in modern statistical modeling. Sufficient dimension reduction (SDR) as an efficient tool aims at reducing the original high dimensional predictors without losing any regression information. Minimum average variance estimation (MAVE) is a popular approach in SDR among others. However, it is not robust to outliers in the response due to the use of least squares. In this study, a robust estimation through regularization with case-specific parameters is proposed to achieve robust estimation and outlier detection simultaneously. Under the nonconvex penalized regression framework, two efficient computational strategies are introduced. Simulation studies and a real data application show the efficacy of the proposed approach. Compared with existing methods, the proposed approach is less sensitive to the choice of initial estimators.

高维已成为现代统计建模中的重要功能。高效降维（SDR）作为一种有效的工具，旨在减少原始的高维预测变量而不会丢失任何回归信息。最小平均方差估计（MAVE）是SDR中的一种流行方法。但是，由于使用最小二乘法，因此对于异常值的响应不具有鲁棒性。在这项研究中，提出了通过针对具体情况的参数进行正则化的鲁棒估计，以同时实现鲁棒估计和离群值检测。在非凸惩罚回归框架下，介绍了两种有效的计算策略。仿真研究和实际数据应用表明了该方法的有效性。与现有方法相比，