Utilização da estatística gradiente e seu refinamento via Bootstrap em modelos lineares simétricos

Abstract

The class of symmetric linear models is a broad class of regression models that encompasses models with heavier tails distributions, as well as lighter tails than the Normal distribution, such as t-Student, Cauchy, Slash and Power Exponential. This class is an alternative to the usual linear regression model in the face of the presence of extremes, which can cause the disproportionate shape in the inference of the adopted parameters. In this work, we will propose a refinement of the statistics of the classic asymptotic tests and the Gradient test in symmetric linear models, using the procedure Bootstrap. To show the importance of the proposal, a simulation study to compare the performance of the statistics of the asymptotic tests in relation to the approximation of their respective levels of significance adopted in different sizes. This study revealed, in general, that the statistics obtained good results using the Bootstrap refinement for small and moderate sample sizes. In order to illustrate the use of the procedures adopted here, if an application to a set of real data, assuming the t-Student distribution with 4 degrees of freedom.