Robust fitting of mixture regression models

The existing methods for fitting mixture regression models assume a normal distribution for error and then estimate the regression parameters by the maximum likelihood estimate (MLE). In this article, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. A real data application is used to illustrate the success of the proposed robust estimation procedure.