Parameter estimation methods, proposals and their comparisons in nonlinear regression models

In this study, the least squares method of the parameter estimation approaches and the weighted least squares method, which is a guiding method for many other parameter estimation methods, have been referred to. Moreover, the maximum likelihood estimation and the quasi likelihood method, which is a modified version of the maximum likelihood estimation has been introduced. By addressing robust estimators, the reasons for developing these methods have been mentioned in the study. Than, the stochastic method, which is developed by Tvrdik et al., has been introduced for parameter estimation. On the other hand, certain points have been realized, whereas some theories and opinions developed as well as some suggestions were made on the approaches. It was shown that algorithms based on Gauss-Newton can be grouped together and a suggestion was made via generalizing the results. Besides, a method based on stochastic search algorithm has been offered as distinct from Gauss-Newton based algorithms. A few processes have been designed and data has been gathered via simulation; moreover, the results of the parameter estimation and standard errors have been identified and were compared by using the methods and approaches mentioned in this study for application. It was found that the proposed methods and parameter estimations that were found were slightly biased and with small standard error.