A different approach to estimate nonlinear regression model using numerical methods

[摘要] This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE's (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

[发布机构] Department of Mathematics, Swetha Institute of Technology and Science, Tirupati, India^1;Department of Mathematics, School of Advanced Sciences, VIT University, Vellore; 632014, India^2;Department of Statistics, S.V.University, Tirupati, India^3

[效力级别] 工业技术

[关键词] Convex minimization;Differential algebraic equations;Gauss-Newton methods;Iterative technique;Non-linear regression;Nonlinear Parameter Estimation;Nonlinear regression models;Weighted least squares