On diagnostics in symmetrical nonlinear models

In this paper, we discuss the extension of some diagnostic procedures to symmetrical nonlinear regression models. This class provides a useful generalization of normal nonlinear regression models since the location parameter continues to be the mean (when it exists) and the error distributions cover both light- and heavy-tailed distributions such as Student-t, logistic, power exponential, generalized Student-t, generalized logistic, contaminated normal, among others. Thus, the models can be checked for robustness and diagnostic methods may be useful tools for an appropriate choice. First, an iterative process for the parameter estimation as well as some inferential results are given. Then, we discuss the calculation of generalized leverage, local influence curvatures and standardized residuals in the symmetrical class extending results obtained for normal nonlinear models. Finally, as illustration of the proposed methods, we consider a data set previously analyzed under normal nonlinear regression models. A diagnostic analysis indicates that a Student-t nonlinear regression model with 4 degrees of freedom seems to fit the data better than the normal nonlinear regression model as well as other symmetrical nonlinear models in the sense of robustness against outlying and influential observations.