A novel perspective for parameter estimation of seemingly unrelated nonlinear regression

Abstract

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.

KEYWORDS:

• Nonlinear regression
• seemingly unrelated nonlinear regression (SUNR)
• parameter estimation
• multi-objective optimization
• soft computing

Acknowledgments

The author would like to thank the anonymous referees and the Editor for their useful comments and suggestions that improved substantially the content and quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).