Estudo sobre os modelos não-lineares simétricos: aspectos inferenciais e aplicações

Abstract

Outliers appear in the analyses of various datasets, which can affect the parameter estimation by distorting the point estimations, for instance. One way to deal with datasets that have outliers is to suppose a distribution for the model erros that possesses heavier tails than those of the normal distribution. Models that suppose that the errors are distributed according to the symmetrical family is an alternative to the normal distributions in these cases, and have been frequently used in the literature, seeing as the models are less sensitive to the presence of annomalies. On the other hand a linear model does not always fit well to the observations of a dataset, hence making it necessary to have a non-linear structure for modelling the data. This piece aims to study non-linear symmetrical models. To accomplish this, different distributions belonging to the symmetrical families are presented, the non-linear symmetrical model is chosen, inferential aspects, iterative processes for the estimation of the chosen model's parameters and some assymptotic results with the estimator and hypothesis test properties are developed. Lastly, applications made to three real datasets are done using the R language.