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Robust algorithms for multiphase regression models

机译：多相回归模型的鲁棒算法

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摘要

This paper proposes a robust procedure for solving multiphase regression problems that is efficient enough to deal with data contaminated by atypical observations due to measurement errors or those drawn from heavy-tailed distributions. Incorporating the expectation and maximization algorithm with the M-estimation technique, we simultaneously derive robust estimates of the change-points and regression parameters, yet as the proposed method is still not resistant to high leverage outliers we further suggest a modified version by first moderately trimming those outliers and then implementing the new procedure for the trimmed data. This study sets up two robust algorithms using the Huber loss function and Tukey's biweight function to respectively replace the least squares criterion in the normality-based expectation and maximization algorithm, illustrating the effectiveness and superiority of the proposed algorithms through extensive simulations and sensitivity analyses. Experimental results show the ability of the proposed method to withstand outliers and heavy-tailed distributions. Moreover, as resistance to high leverage outliers is particularly important due to their devastating effect on fitting a regression model to data, various real-world applications show the practicability of this approach.
机译：本文提出了一种稳健的过程，用于解决多相回归问题，该问题足以应对由于测量误差或从重尾分布绘制的那些引起的由非典型观测污染的数据进行处理。利用M估计技术结合了期望和最大化算法，我们同时推出了变化点和回归参数的强大估计，但由于所提出的方法仍然无法抵抗高杠杆异常值，我们通过首先进行了一个适度的修剪进一步提出了修改的版本那些异常值，然后实现修剪数据的新过程。本研究建立了使用Huber损耗功能和Tukey的双重函数来分别替换基于正常性的期望和最大化算法中的最小二乘标准的两个强大算法，说明了通过广泛的模拟和灵敏度分析的所提出的算法的有效性和优越性。实验结果表明，提出的方法承受异常值和重尾分布的能力。此外，由于对高杠杆异常值的抵抗尤其重要，因此由于它们对数据的损坏效果拟合到数据，各种实际应用展示了这种方法的实用性。

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