Robust variable selection for mixture linear regression models

In this paper, we propose a robust variable selection to estimate and select relevant covariates for the finite mixture of linear regression models by assuming that the error terms follow a Laplace distribution to the data after trimming the high leverage points. We introduce a revised Expectation-maximization (EM) algorithm for numerical computation. Simulation studies indicate that the proposed method is robust to both the high leverage points and outliers in the y-direction, and can obtain a consistent variable selection in the case of outliers or heavy-tail error distribution. Finally, we apply the proposed methodology to analyze a real data.