Misturas finitas de modelos de regressão multivariados assimétricos

Abstract

The usual estimation of regression models in the context of finite mixtures is based on the assumption of normality of errors and, therefore, is sensitive to outliers, heavy tail errors and/or asymmetric errors. In this work two proposals are presented to deal with these issues simultaneously considering finite mixtures of regression models under multivariate distributions of Skew-Normal Mixture Scales (MESN). These approaches allow you to model data with great flexibility while accommodating asymmetry and heavy tails. The main virtue of considering regression models under the MESN class is that they have a good hierarchical representation that allows an easy implementation of inferences. The proposed regression models studied were the classical method Finite Mixtures of Regression Models under the MESN distributions (MR-MF-MESN) and the Finite Mixtures method of Regression Models Experts under the MESN distributions (MoE-MF-MESN). A simple EM-type algorithm was used to perform maximum likelihood inference of the parameters of the proposed models. Simulation studies are presented to compare the two models with respect to the classification of observations and to analyze the convergence of estimates asymptotically. Finally, a real dataset is analyzed, illustrating the usefulness of the proposed methods.