Robust mixture regression model fitting by Laplace distribution

A robust estimation procedure for mixture linear regression models is proposed by assuming that the error terms follow a Laplace distribution. Using the fact that the Laplace distribution can be written as a scale mixture of a normal and a latent distribution, this procedure is implemented by an EM algorithm which incorporates two types of missing information from the mixture class membership and the latent variable. Finite sample performance of the proposed algorithm is evaluated by simulations. The proposed method is compared with other procedures, and a sensitivity study is also conducted based on a real data set.