The traditional estimation of mixture regression models is based on the assumption of normality (symmetry) of component errors and thus is sensitive to outliers, heavy-tailed errors and/or asymmetric errors. In this work we present a proposal to deal with these issues simultaneously in the context of the mixture regression by extending the classic normal model by assuming that the random errors follow a scale mixtures of skew-normal distributions. This approach allows us to model data with great flexibility, accommodating skewness and heavy tails. The main virtue of considering the mixture regression models under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows easy implementation of inference. We develop a simple EM-type algorithm to perform maximum likelihood inference of the parameters of the proposed model. In order to examine the robust aspect of this flexible model against outlying observations, some Electronic supplementary material The online version of this article (

In statistical analysis, particularly in econometrics, the finite mixture of regression models based on the normality assumption is routinely used to analyze censored data. In this work, an extension of this model is proposed by considering scale mixtures of normal distributions (SMN). This approach allows us to model data with great flexibility, accommodating multimodality and heavy tails at the same time. The main virtue of considering the finite mixture of regression models for censored data under the SMN class is that this class of models has a nice hierarchical representation which allows easy implementation of inferences. We develop a simple EM-type algorithm to perform maximum likelihood inference of the parameters in the proposed model. To examine the performance of the proposed method, we present some simulation studies and analyze a real dataset. The proposed algorithm and methods are implemented in the new R package CensMixReg.

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