Statistical Diagnostics for Nonlinear Regression Models Based on Scale Mixtures of Skew-Normal Distributions

The purpose of this paper is to develop diagnostics analysis for nonlinear regression models under scale mixtures of skew-normal distributions (Branco and Dey, 2001). This novel class of models provides a useful generalization of the symmetrical nonlinear regression models (Vanegas and Cysneiros, 2010) since the random terms distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. The main virtue of considering the nonlinear regression model under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows an easy implementation of inference procedures. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented and the observed information matrix is derived analytically. We discuss a score test for testing the homogeneity of the scale parameter and its properties are investigated through Monte Carlo simulations. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. The newly developed procedures are illustrated considering a real data previously analyzed under normal and skew-normal nonlinear regression models.