Modelos de regressão para dados censurados sob a classe de distribuições de misturas de escala normal assimétricas

Abstract

A frequent problem in regression analysis is when the observation of the response variable is censored for some subjects. This occurs in several practical situations, for reasons such as limitations of the measuring equipment or the experimental design. These phenomena can be modeled using statistical and mathematical models. In the framework of censored regression models the random errors are routinely assumed to have a normal distribution, mainly for mathematical convenience. However, this method has been criticized in the literature because of its sensitivity to deviations from the normality assumption. In this dissertation, we first establish a new link between the censored regression model and the class of asymmetric distributions studied by Ferreira et al. [13]. Skew scale mixtures of normal distributions are often used for statistical procedures involving asymmetric data and heavy-tailed. The main virtue of the members of this family of distributions is that they are easy to simulate and also provide expectation-maximization (EM) algorithms for maximum likelihood estimation. In this work, we extend the EM algorithm for the MCEM algorithm for linear regression models censored. The EM-type algorithm has been discussed with an emphasis on the Skew-normal, Skew Student-t-normal, Skew slash and Skew-contaminated normal distributions. The proposed methods are verified through the analysis of several simulation studies and applying in real datasets.