Abstract Partial least squares (PLS) regression is a widely-used regression method for high-dimensional data. However, PLS is not robust to outlying observations since it uses partial information of the variables in a least squares (LS) setting, which is known to be very sensitive to outliers. Several proposals are available which robustify PLS. In this study, our aim is to propose a new partial robust estimator using robust adaptive modified maximum likelihood (RAMML) estimators [1, 2]. The resulting estimators are therefore called partial robust adaptive modified maximum likelihood estimators (PRAMMLs). The distinguished advantage of the PRAMMLs is that they are computationally straightforward. This is because of the fact that they are constructed based on explicitly formulated estimators. The simulation study shows that the PRAMMLs are preferable to PLS and other existing robust alternatives of PLS in terms of the mean squared error (MSE) criterion under different nonnormal error distributions, as well as in the presence of leverage points. The PRAMMLs also give satisfactory results in terms of the empirical influence function and breakdown robustness criteria.

中文翻译：

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一种新的部分鲁棒自适应修正最大似然估计器

摘要 偏最小二乘（PLS）回归是一种广泛用于高维数据的回归方法。然而，PLS 对离群观察并不稳健，因为它在最小二乘 (LS) 设置中使用变量的部分信息，众所周知，该设置对离群值非常敏感。有几个建议可以增强 PLS。在这项研究中，我们的目标是使用鲁棒自适应修正最大似然 (RAMML) 估计器 [1, 2] 提出一种新的部分鲁棒估计器。因此，由此产生的估计量称为部分鲁棒自适应修正最大似然估计量 (PRAMML)。PRAMML 的显着优势在于它们在计算上很简单。这是因为它们是基于明确制定的估计量构建的。模拟研究表明，在不同非正态误差分布下以及存在杠杆点的情况下，就均方误差 (MSE) 标准而言，PRAMML 优于 PLS 和其他现有的 PLS 稳健替代方案。PRAMML 在经验影响函数和击穿稳健性标准方面也给出了令人满意的结果。