Restricted methods in symmetrical linear regression models

In this paper we discuss the problem of testing equality and inequality constraints in symmetrical linear regression models. This class of models includes all symmetric continuous distributions, such as normal, Student-t, Pearson VII, power exponential and logistic, among others. It is commonly used for the analysis of data containing influential or outlying observations with responses supposedly normal. Iterative processes for evaluating the parameters under equality and inequality constraints are presented. The asymptotic null distribution of three asymptotically equivalent one-sided tests is showed to be invariant with the symmetrical error. A sensitivity study to investigate the robustness of the maximum likelihood estimates from some symmetrical models against high leverage and influential observations is presented. An illustrative example with presence of influential observations on the decisions from the statistical tests of different symmetrical models is given. The robustness aspects of such models are also discussed.