Reparameterization of weakly nonlinear regression models with constraints

2016 ◽  
Vol 66 (3) ◽  
Author(s):  
Lubomír Kubáček ◽  
Gejza Wimmer
Keyword(s):  
Nonlinear Regression ◽  
Regression Models ◽  
Confidence Regions ◽  
Weakly Nonlinear ◽  
Nonlinear Regression Models ◽  
Parameter Estimators

AbstractThere are several ways how to redefine the Bates and Watts curvatures in models with constraints. One of possible approaches is based on a reparametrization of models. It enables us to construct linearization regions for the bias of parameter estimators, for the confidence regions, etc., in an easy way.

Confidence regions in singular weakly nonlinear regression models with constraints

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
Lubomír Kubáček
Keyword(s):  
Regression Model ◽  
Nonlinear Regression ◽  
Regression Models ◽  
Confidence Region ◽  
Confidence Regions ◽  
Nonlinear Regression Model ◽  
Weakly Nonlinear ◽  
Nonlinear Regression Models ◽  
Linearized Model ◽  
Confidence Ellipsoid

AbstractIt is rather complicated to construct the confidence region in nonlinear regression model mainly when number of parameters is large. If the nonlinearity of the model is weak, then it is possible, after some modification, to approximate the confidence region by a confidence ellipsoid in the linearized model. The aim of the paper is to propose a solution in singular models with constraints.

Testing Statistical Hypotheses in Singular Weakly Nonlinear Regression Models

2015 ◽  
Vol 65 (2) ◽  
Author(s):  
Lubomír Kubáček
Keyword(s):  
Nonlinear Regression ◽  
Statistical Models ◽  
Regression Models ◽  
Weakly Nonlinear ◽  
Nonlinear Regression Models ◽  
Statistical Hypotheses ◽  
Linear Statistical Models

AbstractWeakly nonlinear hypothesis on parameters in nonlinear regression models can be tested by methods of linear statistical models in some cases. Certain conditions must be satisfied. The aim of the paper is to find them for models without/with constraints on parameters.

scholarly journals Methods to verify parameter equality in nonlinear regression models

2010 ◽  
Vol 67 (2) ◽  
pp. 218-222 ◽  
Author(s):  
Lídia Raquel de Carvalho ◽  
Sheila Zambello de Pinho ◽  
Martha Maria Mischan
Keyword(s):  
Nonlinear Regression ◽  
Regression Models ◽  
Growth Curves ◽  
Original Data ◽  
Minimum Variance ◽  
Ratio Method ◽  
Parameter Estimates ◽  
Nonlinear Regression Models ◽  
Sample Data ◽  
Parameter Estimators

In biologic experiments, in which growth curves are adjusted to sample data, treatments applied to the experimental material can affect the parameter estimates. In these cases the interest is to compare the growth functions, in order to distinguish treatments. Three methods that verify the equality of parameters in nonlinear regression models were compared: (i) developed by Carvalho in 1996, performing ANOVA on estimates of parameters of individual fits; (ii) suggested by Regazzi in 2003, using the likelihood ratio method; and (iii) constructing a pooled variance from individual variances. The parametric tests, F and Tukey, were employed when the parameter estimators were near to present the properties of linear model estimators, that is, unbiasedness, normal distribution and minimum variance. The first and second methods presented similar results, but the third method is simpler in calculations and uses all information contained in the original data.

Linearization Regions in Singular Weakly Nonlinear Regression Models with Constraints

2015 ◽  
Vol 65 (5) ◽  
Author(s):  
Lubomír Kubáček
Keyword(s):  
Nonlinear Regression ◽  
Regression Models ◽  
Weakly Nonlinear ◽  
Nonlinear Regression Models ◽  
Additional Investigation

AbstractA linearization of nonlinear regression models is frequently used in practice. A recognition whether it can be done need some additional investigation. Some problems occur when constraints are involved in the model mainly when the model is singular. One possible solution is given in the paper.

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