The traditional estimation of mixture regression models is based on the assumption of normal error components, making it susceptible to outliers or heavy-tailed errors. A new robust mixture regression model based on the symmetric 𝛼-stable (S 𝛼 S) distribution, by extending the mixture of S 𝛼 S distributions to the regression setting, is proposed. The S 𝛼 S distribution is a heavy-tailed extension of the normal distribution, with the tails’ weight controlled by an additional parameter, 𝛼∈(0,2]. The variance of a S 𝛼 S distribution diverges to infinity when 𝛼<2, and this allows the model to be more robust than competing heavy-tailed distributions such as the t-distribution when the degrees of freedom are larger than 2, which is advantageous because it allows robustness against the gross outliers in the data. The maximum likelihood estimates of the model parameters (except for 𝛼) are obtained using an expectation-maximization (EM) approach, and 𝛼 is estimated via a stochastic EM based on a rejection sampling method. To demonstrate and contrast the proposal with other mixture regression models, real and simulated data are employed.
