A weighted likelihood approach for robust fitting of a finite mixture of linear regression models is proposed. An EM type algorithm and its variant based on the classification likelihood have been developed. The proposed algorithm is characterized by an M-step that is enhanced by the computation of weights aimed at downweighting outliers. The weights are based on the Pearson residuals stemming from the assumption of normality for the error distribution. Formal rules for robust clustering and outlier detection are also defined based on the fitted mixture model. The behavior of the proposed methodologies has been investigated by numerical studies and real data examples in terms of both fitting and classification accuracy and outlier detection.

提出了一种用于线性回归模型有限混合的鲁棒拟合的加权似然方法。已经开发了一种基于分类可能性的EM类型算法及其变体。所提出的算法的特征在于M步，该M步通过针对加权异常值权重的计算来增强。权重基于源自误差分布正态性假设的Pearson残差。还基于拟合的混合模型定义了鲁棒聚类和离群值检测的形式规则。通过数值研究和实际数据示例，从拟合和分类精度以及离群值检测的角度研究了所提出方法的行为。