Nonlinear regression models based on scale mixtures of skew-normal distributions

Abstract

An extension of some standard likelihood based procedures to nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models 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. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented and the observed information matrix is derived analytically. In order to examine the robust aspect of this flexible class against outlying and influential observations, some simulation studies have also been presented. Finally, an illustration of the methodology is given considering a data set previously analyzed under normal and skew-normal nonlinear regression models.