This article presents a robust fuzzy procedure for estimating change-point regression models. We propose incorporating the fuzzy change-point algorithm with the M-estimation technique for robust estimations. The fuzzy c partitions concept is embedded into the change-point regression model so the fuzzy c-regressions and fuzzy c-means clustering can be employed to obtain the estimates of change-points and regression parameters. The M estimation with a robust criterion is used to make the estimators robust to the presence of outliers and heavy-tailed distributions. We create two robust algorithms named FCH and FCT by using Huber’s and Tukey’s functions as the robust criterion respectively. Extensive experiments with numerical and real examples are provided for demonstrating the effectiveness and the superiority of the proposed algorithms. The experimental results show the proposed algorithms are resistant to atypical observations and outperform the existing methods. The proposed FCH and FCT are generally comparable but FCT performs better in the presence of extremely high leverage outliers and heavy-tailed distributions. Real data applications show the practical usefulness of the proposed method.

中文翻译：

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变化点回归模型的鲁棒模糊聚类算法

本文介绍了一种用于估计变化点回归模型的稳健模糊程序。我们建议将模糊变化点算法与 M 估计技术结合起来进行稳健估计。模糊 c 分区概念被嵌入到变化点回归模型中，因此可以使用模糊 c 回归和模糊 c 均值聚类来获得变化点和回归参数的估计值。具有稳健标准的 M 估计用于使估计量对异常值和重尾分布的存在具有稳健性。我们分别使用 Huber 函数和 Tukey 函数作为鲁棒标准，创建了两个鲁棒算法 FCH 和 FCT。提供了具有数值和真实示例的大量实验，以证明所提出算法的有效性和优越性。实验结果表明，所提出的算法能够抵抗非典型观察并优于现有方法。提议的 FCH 和 FCT 通常具有可比性，但 FCT 在存在极高杠杆异常值和重尾分布的情况下表现更好。实际数据应用表明了该方法的实际实用性。