A new method for robust mixture regression.

Finite mixture regression models have been widely used for modelling mixed regression relationships arising from a clustered and thus heterogenous population. The classical normal mixture model, despite its simplicity and wide applicability, may fail in the presence of severe outliers. Using a sparse, case-specific, and scale-dependent mean-shift mixture model parameterization, we propose a robust mixture regression approach for simultaneously conducting outlier detection and robust parameter estimation. A penalized likelihood approach is adopted to induce sparsity among the mean-shift parameters so that the outliers are distinguished from the remainder of the data, and a generalized Expectation-Maximization (EM) algorithm is developed to perform stable and efficient computation. The proposed approach is shown to have strong connections with other robust methods including the trimmed likelihood method and M-estimation approaches. In contrast to several existing methods, the proposed methods show outstanding performance in our simulation studies.