A novel perspective for parameter estimation of seemingly unrelated nonlinear regression

Nonlinear regression is commonly used as a modeling tool to get a functional form between inputs and response variables when the inputs and the responses have a nonlinear relationship. It should be better to compose the predicted nonlinear models with considering correlation between the responses for multi-response data sets. For this purpose, seemingly unrelated nonlinear regression (SUNR) have been widely used in the literature. The parameter estimation procedure of the SUNR is based on nonlinear least squares (NLS) method, based on L2-norm. However, it is possible to use different norms for parameter estimation process. The novelty of this study is presenting the applicability of least absolute deviation (LAD) method, defined in L1-norm, with the NLS method simultaneously for obtaining parameter estimates of the SUNR model in a multi objective perspective. In this study, the proposed multi-objective SUNR model is called MO-SUNR. The optimization of the MO-SUNR model is achieved by using soft computing methods. Two data set examples are given for application purposes of the MO-SUNR model. It is seen from the results that the MO-SUNR provides many alternatively usable compromise parameter estimates through the simultaneous evaluation of the LAD and the NLS methods.