Sliced average third-moment estimation (SATME) is a typical method for sufficient dimension reduction (SDR) based on high-order conditional moment. It is useful, particularly in the scenarios of regression mixtures. However, as SATME uses the third-order conditional moment of the predictors given the response, it may not as robust as some other SDR methods that use lower order moments, say, sliced inverse regression (SIR) and slice average variance estimation (SAVE). Based on the space displacement function, a local influence analysis framework of SATME is constructed including a statistic of influence assessment for the observations. Furthermore, a data-trimming strategy is suggested based on the above influence assessment. The proposed methodologies solve a typical issue that also exists in some other SDR methods. A real-data analysis and simulations are presented.

中文翻译：

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切片平均三阶矩估计的局部影响分析

切片平均三次矩估计（SATME）是一种典型的基于高阶条件矩的充分降维（SDR）方法。它很有用，特别是在回归混合的情况下。然而，由于 SATME 使用给定响应的预测变量的三阶条件矩，它可能不如使用低阶矩的其他一些 SDR 方法稳健，例如切片逆回归 (SIR) 和切片平均方差估计 (SAVE) . 基于空间位移函数，构建了SATME局部影响分析框架，包括对观测的影响评估统计。此外，基于上述影响评估提出了一种数据修剪策略。所提出的方法解决了一些其他 SDR 方法中也存在的典型问题。