Estimação em modelos de regressão linear com ponto de mudança contínuo sob a distribuição t-Student

Abstract

n this work, we present recent results in a statistical research field with a wide range of applications: linear regression models. The normality (symmetry) of random errors is an ordinary assumption in linear models, which may be unrealistic. Thus, we relax the assumption of normality and consider the case of scale mixture of normal regression,which has the normal regression as a particular case. Furthermore, this model is able to capture several non normal behaviors by applying an extra parameter, the degree of freedom, that can control the kurtosis. In addition, we consider 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 change point. In this context, the estimation of the parameters is performed via EM algorithm, and the selection of models is made by using information criteria (SIC and AIC). Finally, numerical examples considering simulated and real data are presented to illustrate the model and the inferential results developed. We believe that this is work will be useful students, researchers and practitioners to be of a great applicability.