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Applications des modèles linéaires et non linéaires : effets fixes, effets aléatoires, ...
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Numéro de l'objet eBay :364844242899
Dernière mise à jour le 05 mai 2024 01:56:58 CEST. Afficher toutes les modificationsAfficher toutes les modifications
Caractéristiques de l'objet
- État
- Book Title
- Applications of Linear and Nonlinear Models : Fixed Effects, Rand
- ISBN
- 9783030945978
- Publication Year
- 2022
- Series
- Springer Geophysics Ser.
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Publication Name
- Applications of Linear and Nonlinear Models : Fixed Effects, Random Effects, and Total Least Squares
- Item Length
- 9.3in
- Publisher
- Springer International Publishing A&G
- Item Width
- 6.1in
- Item Weight
- 77.2 Oz
- Number of Pages
- Xxv, 1113 Pages
À propos de ce produit
Product Information
Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. The fifth problem of algebraic regression, the system of conditional equations of homogeneous and inhomogeneous type, is formulated. An analogue is the inhomogeneous general linear Gauss-Markov model with fixed and random effects, also called mixed model. Collocation is an example. Another speciality is our sixth problem of probabilistic regression, the model "errors-in-variable", also called Total Least Squares, namely SIMEX and SYMEX developed by Carroll-Cook-Stefanski-Polzehl-Zwanzig. Another speciality is the treatment of the three-dimensional datum transformation and its relation to the Procrustes Algorithm. The sixth problem of generalized algebraic regression is the system of conditional equations with unknowns, also called Gauss-Helmert model. A new method of an algebraic solution technique, the concept of Groebner Basis and Multipolynomial Resultant is finally presented, illustrating polynomial nonlinear equations. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm Throughout we give numerous examples and present various test computations. Our reference list includes more than 3000 references, books and papers. This book is a source of knowledge and inspiration not only for geodesists and mathematicians, but also for engineers in general, as well as natural scientists and economists. Inference on effects which result in observations via linear and nonlinear functions is a general task in science. The authors provide a comprehensive in-depth treatise on the analysis and solution of such problems. I wish all readers of this brilliant encyclopaedic book this pleasure and much benefit. Prof. Dr. Harro Walk Institute of Stochastics and Applications, Universität Stuttgart, Germany.
Product Identifiers
Publisher
Springer International Publishing A&G
ISBN-10
3030945979
ISBN-13
9783030945978
eBay Product ID (ePID)
12057249246
Product Key Features
Publication Name
Applications of Linear and Nonlinear Models : Fixed Effects, Random Effects, and Total Least Squares
Format
Hardcover
Language
English
Publication Year
2022
Series
Springer Geophysics Ser.
Type
Textbook
Number of Pages
Xxv, 1113 Pages
Dimensions
Item Length
9.3in
Item Width
6.1in
Item Weight
77.2 Oz
Additional Product Features
Number of Volumes
1 Vol.
Lc Classification Number
Qe1-996.5
Edition Number
2
Table of Content
The First Problem of Algebraic Regression.- The First problem of probabilistic regression - the bias problem.- The second problem of algebraic regression - inconsistent system of linear observational equations.- The second problem of probabilistic regression- special Gauss-Markov model without datum defect - Setup of BLUUE for the moments of first order and of BIQUUE for the central moment of second order.- The third problem of probabilistic regression - special Gauss - Markov model with datum problem -Setup of BLUMBE and BLE for the moments of first order and of BIQUUE and BIQE for the central moment of second order.
Copyright Date
2022
Topic
Algebra / Linear, Probability & Statistics / General, Earth Sciences / Geology, General
Dewey Decimal
550.015118
Dewey Edition
23
Illustrated
Yes
Genre
Science, Mathematics
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Numéro de l'objet eBay :364844242899
Dernière mise à jour le 05 mai 2024 01:56:58 CEST. Afficher toutes les modificationsAfficher toutes les modifications
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Lieu où se trouve l'objet :
Jessup, Maryland, États-Unis
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