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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Geowissenschaft Geologie Applications of Linear and Nonlinear Models
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Applications of Linear and Nonlinear Models
Erik Grafarend (Gebundene Ausgabe, Englisch)
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Beschreibung
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.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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
05.08.2012
Sprache
Englisch
EAN
9783642222405
Herausgeber
Springer Berlin
Sonderedition
Nein
Autor
Erik Grafarend
Seitenanzahl
1016
Einbandart
Gebundene Ausgabe
Buch Untertitel
Fixed Effects, Random Effects, and Total Least Squares
Schlagwörter
BLUUE, Fixed effects, Geodesy, LESS, Linear Models, Nonlinear Models, Random effects, Statistics, Total least squares, matrix theory
Thema-Inhalt
PHVG - Geophysik
PBF - Algebra
PBT - Wahrscheinlichkeitsrechnung und Statistik
Höhe
235 mm
Breite
15.5 cm
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