Robust mixture regression modeling based on scale mixtures of skew-normal distributions

• Camila B. Zeller ^[1] ; Celso R. B. Cabral ^[2] ; Víctor H. Lachos ^[3]
  1. [1] Universidade Federal de Juiz de Fora

     Universidade Federal de Juiz de Fora

     Brasil

     
  2. [2] Universidade Federal do Amazonas

     Universidade Federal do Amazonas

     Brasil

     
  3. [3] Universidade Estadual de Campinas

     Universidade Estadual de Campinas

     Brasil

     

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 25, Nº. 2, 2016, págs. 375-396
• Idioma: inglés
• DOI: 10.1007/s11749-015-0460-4
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 simulation studies are also presented. Finally, a real data set is analyzed, illustrating the usefulness of the proposed method.