Nonlinear Statistical Models

ISBN-13: 9789048142620 / Angielski / Miękka / 2010 / 260 str.

Andrej Pazman

Opis

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.

Spis treści

Introduction. 1. Linear regression models. 2. Linear methods in nonlinear regression models. 3. Univariate regression models. 4. The structure of a multivariate nonlinear regression model and properties of L2 estimators. 5. Nonlinear regression models: computation of estimators and curvatures. 6. Local approximations of probability densities and moments of estimators. 7. Global approximations of densities of L2 estimators. 8. Statistical consequences of global approximations especially in flat models. 9. Nonlinear exponential families. References. Basic symbols. Subject index.