Semiparametric mixture of linear regressions with nonparametric Gaussian scale mixture errors

In finite mixture of regression models, normal assumption for the errors of each regression component is typically adopted. Though this common assumption is theoretically and computationally convenient, it often produces inefficient and undesirable estimates which undermine the applicability of the model particularly in the presence of outliers. To reduce these defects, we propose to use nonparametric Gaussian scale mixture distributions for component error distributions. By this means, we can lessen the risk of misspecification and obtain robust estimators. In this paper, we study the identifiability of the proposed model and develop a feasible estimating algorithm. Numerical studies including simulation studies and real data analysis to demonstrate the performance of the proposed method are also presented.