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

An extension of some standard likelihood based procedures to nonlinear regression models under scale mixtures of skew-normal distributions is developed. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models since the error distributions cover both skewness and heavy-tailed distributions such as the skew-t, skew-slash and the skew-contaminated normal distributions. The main advantage of these class of distributions is that they have a nice hierarchical representation which allows easy implementation of inference. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented and the observed information matrix for obtaining the asymptotic covariance matrix is derived analytically. With the aim of identifying atypical observations and/or model misspecification a brief discussion of the standardized residuals is given. Finally, an illustration of the methodology is given considering a data set previously analyzed under skew-normal nonlinear regression models. Our analysis indicates that a skew-t nonlinear regression model with 3 degrees of freedom seems to fit the data better than the skew-normal nonlinear regression model as well as other asymmetrical nonlinear models in the sense of robustness against outlying observations.