Robust Regression Modeling for Censored Data Based on Mixtures of Student-t Distributions

Víctor H. Lachos
Luis Benites Sánchez
Celso R. B. Cabral

In the framework of censored regression models, the distribution of the error terms departs significantly from normality, for instance, in the presence of heavy tails, skewness and/or atypical observations. In this paper we extend the censored linear regression model with normal errors to the case where the random errors follow a finite mixture of Student-t distributions. Thisapproach allows us to model data with great flexibility, accommodating multimodality, heavy tails and also skewness depending on the structure of the mixture components. We develop an analytically simple and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of the truncated Student-t distributions. The efficacy of the method is verified through the analysis of simulated datasets and modeling a censored real dataset first analyzed under normal and Student-t errors. The proposed algorithm and methods are implemented in the R package CensMixReg().

Censored regression model
EM-type algorithms
Finite mixture models
Heavy- tails
Tobit model