TY - JOUR
T1 - Regression modeling of censored data based on compound scale mixtures of normal distributions
AU - Benites, Luis
AU - Zeller, Camila B.
AU - Bolfarine, Heleno
AU - Lachos, Víctor H.
N1 - Publisher Copyright:
© Brazilian Statistical Association, 2023.
PY - 2023/6
Y1 - 2023/6
N2 - In the framework of censored regression models, the distribution of the error term can depart significantly from normality, for instance, due to the presence of multimodality, skewness and/or atypical observations. In this paper we propose a novel censored linear regression model where the random errors follow a finite mixture of scale mixtures of normal (SMN) distribution. The SMN is an attractive class of symmetrical heavy-tailed densities that includes the normal, Student-t, slash and the contaminated normal distribution as special cases. This approach allows us to model data with great flexibility, accommodating simultaneously multimodality, heavy tails and skewness depending on the structure of the mixture components. We develop an analyt-ically tractable and efficient EM-type algorithm for iteratively computing the maximum likelihood estimates of the parameters, with standard errors and prediction of the censored values as a by-products. The proposed algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated SMN distributions. The efficacy of the method is verified through the analysis of simulated and real datasets. The methodology addressed in this paper is implementeIn the framework of censored regression models, the distribution of the
error term can depart significantly from normality, for instance, due to
the presence of multimodality, skewness and/or atypical observations.
In this paper we propose a novel censored linear regression model where
the random errors follow a finite mixture of scale mixtures of normal
(SMN) distribution. The SMN is an attractive class of symmetrical
heavy-tailed densities that includes the normal, Student-t, slash and
the contaminated normal distribution as special cases. This approach
allows us to model data with great flexibility, accommodating
simultaneously multimodality, heavy tails and skewness depending on the
structure of the mixture components. We develop an analytically
tractable and efficient EM-type algorithm for iteratively computing the
maximum likelihood estimates of the parameters, with standard errors and
prediction of the censored values as a by-products. The proposed
algorithm has closed-form expressions at the E-step, that rely on
formulas for the mean and variance of the truncated SMN distributions.
The efficacy of the method is verified through the analysis of simulated
and real datasets. The methodology addressed in this paper is
implemented in the R package CensMixRegd in the R package CensMixReg.
AB - In the framework of censored regression models, the distribution of the error term can depart significantly from normality, for instance, due to the presence of multimodality, skewness and/or atypical observations. In this paper we propose a novel censored linear regression model where the random errors follow a finite mixture of scale mixtures of normal (SMN) distribution. The SMN is an attractive class of symmetrical heavy-tailed densities that includes the normal, Student-t, slash and the contaminated normal distribution as special cases. This approach allows us to model data with great flexibility, accommodating simultaneously multimodality, heavy tails and skewness depending on the structure of the mixture components. We develop an analyt-ically tractable and efficient EM-type algorithm for iteratively computing the maximum likelihood estimates of the parameters, with standard errors and prediction of the censored values as a by-products. The proposed algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated SMN distributions. The efficacy of the method is verified through the analysis of simulated and real datasets. The methodology addressed in this paper is implementeIn the framework of censored regression models, the distribution of the
error term can depart significantly from normality, for instance, due to
the presence of multimodality, skewness and/or atypical observations.
In this paper we propose a novel censored linear regression model where
the random errors follow a finite mixture of scale mixtures of normal
(SMN) distribution. The SMN is an attractive class of symmetrical
heavy-tailed densities that includes the normal, Student-t, slash and
the contaminated normal distribution as special cases. This approach
allows us to model data with great flexibility, accommodating
simultaneously multimodality, heavy tails and skewness depending on the
structure of the mixture components. We develop an analytically
tractable and efficient EM-type algorithm for iteratively computing the
maximum likelihood estimates of the parameters, with standard errors and
prediction of the censored values as a by-products. The proposed
algorithm has closed-form expressions at the E-step, that rely on
formulas for the mean and variance of the truncated SMN distributions.
The efficacy of the method is verified through the analysis of simulated
and real datasets. The methodology addressed in this paper is
implemented in the R package CensMixRegd in the R package CensMixReg.
KW - Censored regression model
KW - EM-type algorithms
KW - finite mixture models
KW - heavy-tails distributions
KW - limit of detection
KW - Tobit model
KW - Modelo de regresión censurada
KW - Algoritmos de tipo EM
KW - Modelos de mezclas finitas
KW - distribuciones de colas pesadas
KW - Límite de detección
KW - Modelo Tobit
UR - http://www.scopus.com/inward/record.url?scp=85170058005&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/a09cab2f-b29f-3c26-b125-4379e7eee494/
U2 - 10.1214/22-BJPS551
DO - 10.1214/22-BJPS551
M3 - Article in a journal
AN - SCOPUS:85170058005
SN - 0103-0752
VL - 37
SP - 282
EP - 312
JO - Brazilian Journal of Probability and Statistics
JF - Brazilian Journal of Probability and Statistics
IS - 2
ER -