Nonlinear Statistical Models
Published on 30. June 1993
Book
Hardback
X, 260 pages
978-0-7923-2247-4 (ISBN)
Description
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.
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.
More details
Series
Edition
1993 ed.
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
X, 260 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 20 mm
Weight
579 gr
ISBN-13
978-0-7923-2247-4 (9780792322474)
DOI
10.1007/978-94-017-2450-0
Schweitzer Classification
Other editions
Additional editions
Person
Luc Pronzato is Directeur de Recherche at CNRS (French National Center for Scientific Research). From 2008 to 2011 he directed the I3S Laboratory (Informatique, Signaux et Systèmes, Sophia-Antipolis), University of Nice-Sophia-Antipolis/CNRS, where he is still working. He his the co-author of the books Identification of Parametric Models from Experimental Data (with Eric Walter, Springer, 1997) and Dynamical Search: Applications of Dynamical Systems in Search and Optimization (with Henry P. Wynn and Anatoly A. Zhigljavsky, Chapman & Hall/CRC Press, 2000).
Andrej P\'azman is Professor of Probability and Statistics at the Faculty of Mathematics, Physics and Informatics, Comenius University in Bratislava, Slovakia. He has been Head of the Department of Probability and Statistics (1992-1998) and Head of the Section of Mathematics of his faculty (1999-2001), and he is an elected member of the Learned Society of the Slovak Academy of Sciences. He is the author of the books Foundations of Optimum Experimental Design (Reidel, Kluwer group, 1986) and Nonlinear Statistical Models (Kluwer, 1993).
Content
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.