Nonlinear statistical modelling is an area of growing importance. This monograph presents mostly new results and methods concerning the nonlinear regression model.
Among the aspects which are considered are linear properties of nonlinear models, multivariate nonlinear regression, intrinsic and parameter effect curvature, algorithms for calculating the L2-estimator and both local and global approximation. In addition to this a chapter has been added on the large topic of nonlinear exponential families.
The volume will be of interest to both experts in the field of nonlinear statistical modelling and to those working in the identification of models and optimization, as well as to statisticians in general.
Author(s): Andrej Pázman (auth.)
Series: Mathematics and Its Applications 254
Edition: 1
Publisher: Springer Netherlands
Year: 1993
Language: English
Pages: 260
Tags: Probability Theory and Stochastic Processes
Front Matter....Pages i-ix
Introduction....Pages 1-6
Linear regression models....Pages 7-33
Linear methods in nonlinear regression models....Pages 34-54
Univariate regression models....Pages 55-79
The structure of a multivariate nonlinear regression model and properties of L 2 estimators....Pages 80-112
Nonlinear regression models: computation of estimators and curvatures....Pages 113-130
Local approximations of probability densities and moments of estimators....Pages 131-153
Global approximations of densities of L 2 estimators....Pages 154-191
Statistical consequences of global approximations especially in flat models....Pages 192-214
Nonlinear exponential families....Pages 215-247
Back Matter....Pages 248-259
