TY - JOUR
T1 - Linear regression models using finite mixtures of skew heavy-tailed distributions
AU - Benites, Luis
AU - Maehara, Rocío
AU - Lachos, Victor H.
AU - Bolfarine, Heleno
N1 - Publisher Copyright:
Chilean Statistical Society – Sociedad Chilena de Estadística.
PY - 2019/4
Y1 - 2019/4
N2 - 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, skew-t, 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.
AB - 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, skew-t, 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.
KW - ECME algorithm
KW - Mixture model
KW - Non-normal error distribution
KW - Scale mixtures of skew-normal distributions
UR - http://www.scopus.com/inward/record.url?scp=85087643635&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85087643635
SN - 0718-7912
VL - 10
SP - 21
EP - 40
JO - Chilean Journal of Statistics
JF - Chilean Journal of Statistics
IS - 1
ER -