Improving the Performance of Least Squares Estimator in a Nonlinear Regression Model

2020 ◽  
pp. 492-502
Author(s):  
Janjira Piladaeng ◽  
Supranee Lisawadi ◽  
Syed Ejaz Ahmed
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Least Squares Estimator ◽  
Nonlinear Regression Model

scholarly journals A Monograph on Nonlinear Regression Models

2018 ◽  
Vol 7 (4.10) ◽  
pp. 543
Author(s):  
B. Mahaboob ◽  
B. Venkateswarlu ◽  
C. Narayana ◽  
J. Ravi sankar ◽  
P. Balasiddamuni
Keyword(s):  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Nonlinear Models ◽  
Nonlinear Least Squares ◽  
Error Variance ◽  
Ordinary Least Squares ◽  
Parameter Estimates ◽  
Nonlinear Regression Model ◽  
Nonlinear Regression Models

This research article uses Matrix Calculus techniques to study least squares application of nonlinear regression model, sampling distributions of nonlinear least squares estimators of regression parametric vector and error variance and testing of general nonlinear hypothesis on parameters of nonlinear regression model. Arthipova Irina et.al [1], in this paper, discussed some examples of different nonlinear models and the application of OLS (Ordinary Least Squares). MA Tabati et.al (2), proposed a robust alternative technique to OLS nonlinear regression method which provide accurate parameter estimates when outliers and/or influential observations are present. Xu Zheng et.al [3] presented new parametric tests for heteroscedasticity in nonlinear and nonparametric models.  

scholarly journals On the regularization of singular c-optimal designs

2009 ◽  
Vol 59 (5) ◽  
Author(s):  
Luc Pronzato
Keyword(s):  
Optimal Design ◽  
Asymptotic Normality ◽  
Regression Model ◽  
Least Squares ◽  
Nonlinear Regression ◽  
Scalar Function ◽  
Optimal Designs ◽  
Nonlinear Regression Model ◽  
True Value ◽  
Finite Space

AbstractWe consider the design of c-optimal experiments for the estimation of a scalar function h(θ) of the parameters θ in a nonlinear regression model. A c-optimal design ξ* may be singular, and we derive conditions ensuring the asymptotic normality of the Least-Squares estimator of h(θ) for a singular design over a finite space. As illustrated by an example, the singular designs for which asymptotic normality holds typically depend on the unknown true value of θ, which makes singular c-optimal designs of no practical use in nonlinear situations. Some simple alternatives are then suggested for constructing nonsingular designs that approach a c-optimal design under some conditions.

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