Robust mixture regression via an asymmetric exponential power distribution

Finite mixture of linear regression (FMLR) models are an efficient tool to fit the unobserved heterogeneous relationships. The parameter estimation of FMLR models is usually based on the normality assumption, but it is very sensitive to outliers. Meanwhile, the traditional robust methods often need to assume a specific error distribution, and are not adaptive to dataset. In this paper, a robust estimation procedure for FMLR models is proposed by assuming that the error terms follow an asymmetric exponential power distribution, including normal distribution, skew-normal distribution, generalized error distribution, Laplace distribution, asymmetric Laplace distribution, and uniform distribution as special cases. The proposed method can select the suitable loss function from a broad class in a data driven fashion. Under some conditions, the asymptotic properties of proposed method are established. In addition, an efficient EM algorithm is introduced to implement the proposed methodology. The finite sample performance of the proposed approach is illustrated via some numerical simulations. Finally, we apply the proposed methodology to analyze a tone perception data.