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By modeling the obtained data, the estimation of the next step gains importance, specifically in applied basic sciences, such as physics, chemistry, engineering, medicine and space sciences. Although these data sets can be modeled by using linear models, the generated models are often specified by nonlinear functions, since they are derived from solving the systems of differential equations. For instance, the orbit of a spacecraft or a celestial body is generally determined by nonlinear regression models. Therefore, reliable estimation of the parameters is important for the accurate estimation of the orbit. In regression analysis, the multicollinearity leads to unstable and imprecise estimation of the model parameters. This causes the parameter estimates to be misinterpreted. In this study, a new approach to parameter estimation is presented in the case of multicollinearity in nonlinear regression models. The validity of the proposed approach was tested with the simulation study. Thus, a predictive method to have more stable and reliable parameter estimates in nonlinear regression models that are used in various fields of science is gained to the literature.

A new parameter estimation technique using prior information of parameters in nonlinear model with multicollinear data