Convergence Problem in Nonlinear Regression for Parameter Estimation

Abstract

The purpose of this research is to study three effective factors for convergence problem in nonlinearregression parameter estimation : 1) choice of initial value, considering from : Fekedulegn,s method andGrid Search, 2) distribution of data, considering from : Negative Exponential and Monomolecular and 3)sample size : n =20 , n=30 , n=50 and n =100 respectively. Simulations was performed and repeated 500times for each scenario. The result showed that in most situations, when the sample size increase from n=20to n=100 Gauss Newton method, Marquardt and Newton method will make no difference in percent ofconvergence to parameter and the number of average iteration, namely, when the sample size increase, itwill make percent of convergence to parameter increase almost 100 percent. In addition, when the samplesize increase from n=20 to n=100, choice of different initial value does not effect for convergence toparameter. From this research the best method is Marquardt by using Grid Search. It make percent ofconvergence to parameter and the number of average iteration equal to 100 percent and 39.58 iterationsin Negative Exponential model and equal to 98 percent and 47.98 iterations in Monomolecular modelrespectively.

Keywords : Nonlinear Regression / Convergence Problem / Parameter Estimation