Modelos de regressão com ponto de mudança contínuo para dados censurados sob distribuições simétricas

Abstract

In this work, we present recent results in a research area of ​​Statistics with an enormous possibility of applications, which are linear regression models for censored data. The normality of random errors is a routine assumption in linear models, which may be unrealistic. Thus, we relax the normality assumption by considering that random errors follow a normal scale mixed distribution, for example, the t-Student distribution. This distribution includes the normal distribution as a special case and provides flexibility in capturing a wide variety of non-normal behavior by simply adding a parameter, called the degree of freedom, that controls kurtosis. Furthermore, we consider the fact that the same linear regression model may not be valid for an entire set of censored data. That is, the model can change after a specific point that, in general, is unknown, and called the turning point. In this context, the estimation of the model parameters will be via the EM algorithm, and the model selection will be carried out through the information criteria (SIC and AIC). Thus, the main objective of this work is to study some aspects of estimation in linear regression models with change point for censored data under symmetrical distributions. Finally, numerical examples considering simulated and real data are presented to illustrate the model and the inferential results developed.