Computation of nonlinear least squares estimator and maximum likelihood using principles in matrix calculus

14th International Conference on Science, Engineering and Technology

自然科学;工业技术

Mahaboob, B.^1 ; Venkateswarlu, B.^2 ; Ravi Sankar, J.^1 ; Balasiddamuni, P.^3

Department of Mathematics, Swetha Institute of Technology and Science, Tirupati

Andhra Pradesh, India^1

Department of Mathematics, School of Advanced Sciences, VIT University, Vellore

632014, India^2

Department of Statistics, S.V.University, Tirupati

Andhra Pradesh, India^3

关键词: Analytic technique;    Empirical process;    Least squares estimation;    Maximum likelihood estimators (MLE);    Non-linear least squares;    Non-linear regression;    Nonlinear regression models;    Optimization techniques;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/263/4/042125/pdf
DOI  :  10.1088/1757-899X/263/4/042125

来源: IOP

【 摘 要 】

This paper uses matrix calculus techniques to obtain Nonlinear Least Squares Estimator (NLSE), Maximum Likelihood Estimator (MLE) and Linear Pseudo model for nonlinear regression model. David Pollard and Peter Radchenko [1] explained analytic techniques to compute the NLSE. However the present research paper introduces an innovative method to compute the NLSE using principles in multivariate calculus. This study is concerned with very new optimization techniques used to compute MLE and NLSE. Anh [2] derived NLSE and MLE of a heteroscedatistic regression model. Lemcoff [3] discussed a procedure to get linear pseudo model for nonlinear regression model. In this research article a new technique is developed to get the linear pseudo model for nonlinear regression model using multivariate calculus. The linear pseudo model of Edmond Malinvaud [4] has been explained in a very different way in this paper. David Pollard et.al used empirical process techniques to study the asymptotic of the LSE (Least-squares estimation) for the fitting of nonlinear regression function in 2006. In Jae Myung [13] provided a go conceptual for Maximum likelihood estimation in his work "Tutorial on maximum likelihood estimation.