T distribution-based robust semiparametric mixture regression model

Abstract

Semiparametric mixture of regression (SMR) models provide a popular and flexible framework for modeling heterogeneous data that violates some of the parametric assumptions assumed in traditional finite mixture of regressions models. The majority of applications of SMR models assume normality for their error terms. As is well known, Gaussian distribution is sensitive to outliers or heavy-tailed distribution. In this article, we propose a more robust approach of SMR by modeling the error distribution as t distributions. By combining the EM algorithm and kernel density estimator, two algorithms are proposed to fit the robust SMR models and are proven to monotonically increase the likelihood function. We further investigate a modified version based on trimming for high leverage outliers. In real applications, a data adaptive mechanism is discussed to choose the degrees of freedom. A simulation study and three real data analyses show the superiority of the new methodology.