Nonlinear Statistical Models - Andrej Pázman

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Résumé :
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.

Biographie:
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 Syst?mes, 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)....

Sommaire:
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.