Modelo linear normal assimétrico aplicado

Abstract

At this work, we present recent results in a statistical research area with a huge possibility of applications, which are linear regression models. The normality (symmetry) of random errors is an ordinary assumption in linear models, which may be unrealistic. So, we unwind the assumption of normality considering that random errors follow a normal asymmetrical distribution. This distribution includes the normal distribution as a special case and provides flexibility in capturing a wide variety of not normal behaviors, by simply adding a parameter that controls the degree of asymmetry. Exploring statistical properties of the model considered, we implemented the algorithm EM that provides some advantages over direct maximization of the log-likelihood function. In a second stage of this work, we considered the fact that the same linear regression model may not be valid for an entire set of data. Therefore, the model can be changed after a specific point which, in general, is unknown, and named as the changing point. In this context, the estimation of the model parameters will be via algorithm EM, the selection of models and detection of the changing point will be realized by using information criteria (SIC and AIC). In this way, the main contribution of this work is to study the problem of the changing point associated with the regression model on the asymmetry context, extending in a way some results developed by Chen (1998), Chen and Gupta (2001), Osorio and Galea (2005), Zeller et al. (2011) and Arellano et al. (2013), for example. It is hoped that this work will be useful to awakening the interest of students, researchers and professionals to the subject, which we believe to be of a great applicability.