Robust mixtures of regressions models

Abstract

In the fitting of mixtures of linear regression models, the normal assumption has been traditionally used for the error term and then the regression parameters are estimated by the maximum likelihood estimate (MLE) using the EM algorithm. Under the normal assumption, the M step of the EM algorithm uses a weighted least squares estimate (LSE) for the regression parameters. It is well known that the LSE is sensitive to outliers or heavy tailed error distributions. In this report, we propose a robust mixture of linear regression model, which replaces the least square criterion with some robust criteria in the M step of the EM algorithm. In addition, we will use a simulation study to demonstrate how sensitive the traditional mixture regression estimation method is to outliers or heavy tailed error distributions and compare it with our proposed robust mixture regression estimation method. Based on our empirical studies, our proposed robust estimation method works comparably to the traditional estimation method when there are no outliers and the error is normally distributed but is much better if there are outliers or the error has heavy tails (such as t-distribution). A real data set application is also provided to illustrate the effectiveness of our proposed methodology.