A robust class of homoscedastic nonlinear regression models

Abstract

In this paper, we examine a nonlinear regression (NLR) model with homoscedastic errors which follows a flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The objective of using this family is to develop a robust NLR model. The TP-SMN is a rich class of distributions that covers symmetric/asymmetric and lightly/heavy-tailed distributions and is an alternative family to the well-known scale mixtures of skew-normal (SMSN) family studied by Branco and Dey [35]. A key feature of this study is using a new suitable hierarchical representation of the family to obtain maximum-likelihood estimates of model parameters via an EM-type algorithm. The performances of the proposed robust model are demonstrated using simulated and some natural real datasets and also compared to other well-known NLR models.