🤖 AI Summary
This study addresses the sensitivity of traditional semiparametric mixture regression models to outliers and heavy-tailed errors, which stems from their reliance on Gaussian error assumptions and often leads to non-robust estimation. To overcome this limitation, the paper introduces, for the first time, a contaminated Gaussian distribution into the semiparametric mixture regression framework, yielding a model that simultaneously achieves robustness, flexibility, and clustering capability. Parameter estimation is carried out via an EM algorithm, while the ECM algorithm combined with local kernel likelihood methods handles the nonparametric components. This integrated approach enables concurrent model fitting, cluster analysis, and outlier detection. Extensive simulations and real-data analyses demonstrate that the proposed method substantially enhances robustness against outliers without compromising model expressiveness, offering strong theoretical and practical value.
📝 Abstract
Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the Gaussian assumption of the component error distributions. Thus, their estimation is sensitive to outliers and heavy-tailed error distributions. In this paper, we propose semi- and non-parametric contaminated Gaussian mixture of regressions to robustly estimate the parametric and/or non-parametric terms of the models in the presence of mild outliers. The virtue of using a contaminated Gaussian error distribution is that we can simultaneously perform model-based clustering of observations and model-based outlier detection. We propose two algorithms, an expectation-maximization (EM)-type algorithm and an expectation-conditional-maximization (ECM)-type algorithm, to perform maximum likelihood and local-likelihood kernel estimation of the parametric and non-parametric of the proposed models, respectively. The robustness of the proposed models is examined using an extensive simulation study. The practical utility of the proposed models is demonstrated using real data.