Linear regression models using finite mixtures of skew heavy-tailed distributions

Luis Benites, Rocío Maehara, Victor H. Lachos, Heleno Bolfarine

Research output: Contribution to journalArticle in a journalpeer-review

3 Scopus citations


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.
Original languageEnglish
Pages (from-to)21-40
Number of pages20
JournalChilean Journal of Statistics
Issue number1
StatePublished - 15 Apr 2019

Bibliographical note

Publisher Copyright:
Chilean Statistical Society – Sociedad Chilena de Estadística.


  • ECME algorithm
  • Mixture model
  • Non-normal error distribution
  • Scale mixtures of skew-normal distributions


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