## Resumen

In this paper, we propose a regression model based on the assumption that the error term follows a mixture of normal distributions. Specifically, we consider a finite scale mixture of skew-normal distributions, a rich family that contains the skew-normal, skewt,

skew-slash and skew-contaminated normal distributions as members. This model allows us to describe data with high flexibility, simultaneously accommodating multimodality, skewness and heavy tails. We develop a simple EM-type algorithm to perform maximum

likelihood inference of the parameters of the proposed model with closed-form expressions for both E- and M-steps. Furthermore, the observed information matrix is derived analytically to account for the corresponding standard errors and a bootstrap procedure is implemented to test the number of components in the mixture. The practical utility of the new model is illustrated with a real dataset and several simulation studies. The proposed algorithm and methods are implemented in an R package named FMsmsnReg.

skew-slash and skew-contaminated normal distributions as members. This model allows us to describe data with high flexibility, simultaneously accommodating multimodality, skewness and heavy tails. We develop a simple EM-type algorithm to perform maximum

likelihood inference of the parameters of the proposed model with closed-form expressions for both E- and M-steps. Furthermore, the observed information matrix is derived analytically to account for the corresponding standard errors and a bootstrap procedure is implemented to test the number of components in the mixture. The practical utility of the new model is illustrated with a real dataset and several simulation studies. The proposed algorithm and methods are implemented in an R package named FMsmsnReg.

Idioma original | Inglés |
---|---|

Páginas (desde-hasta) | 21-40 |

Número de páginas | 20 |

Publicación | Chilean Journal of Statistics |

Volumen | 10 |

N.º | 1 |

Estado | Publicada - 15 abr. 2019 |

### Nota bibliográfica

Funding Information:The authors thank the Editors and Reviewers for their constructive comments on an earlier version of this manuscript. Luis Benites and Roćıo Maehara acknowledges support from CNPq-Brazil. Victor H. Lachos was supported from CNPq-Brazil (Grant 306334/2015-1). Partial support from CAPES is also acknowledged.

Publisher Copyright:

Chilean Statistical Society – Sociedad Chilena de Estadística.