Estimation methods of nonlinear regression models

Abstract

Nonlinear regression models have been a subject of an intensive investigation in recent years and they have wide uses in applied sciences namely Medicine, Forensic Science, Food Science, Information Science, Applied Ecology, Agronomy, Sports Science and Space Science. This research article mainly focuses on some important and innovative nonlinear estimation techniques of parameters of nonlinear regression models based on principles in matrix differentiation. The methods depicted here are principle of least squares, linear approximation method, and MLE estimation method. Oral Capps, Jr, (see [1]), in his research paper presented a theoretical discussion and some empirical results using maximum likely-hood (ML) method and iterative version of Zellner's seemingly unrelated regression (IZEF) method in the estimation of a non linear system of demand equations when the disturbance terms are both contemporaneously and serially correlated. S. Neal, (see [3]), in his research article considered a discrete real-time nonlinear estimation problem using a least square criterion and derived a sequential algorithm which follows consideration of second order nonlinearities in system measurements. Besides some alternative nonlinear estimation techniques were discussed and examples were given which compare the various estimation algorithms. In 2003, Thomas Schon (see [4]), in his thesis, made a discussion on how to use convex optimization for solving the estimation problem.