Nonlinear Statistical Models

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 L 2 -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. 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