APPLICATIONS OF LINEAR AND NONLINEAR MODELS by Erik Grafarend, Joseph L. Awange ( 9783642222405 )

Item Details

Title:

APPLICATIONS OF LINEAR AND NONLINEAR MODELS
FIXED EFFECTS, RANDOM EFFECTS, AND TOTAL LEAST SQUARES

By:

Format:

Hardback

List price:	£249.99
We currently do not stock this item, please contact the publisher directly for further information.

ISBN 10:

3642222404

ISBN 13:

9783642222405

Publisher:

SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG

Pub. date:

5 August, 2012

Edition:

2012 ed.

Pages:

1016

Description:

This book offers a thorough treatment of the 'Grand Universe' of linear and weakly nonlinear regression models, from an algebraic view as well as a stochastic one. Includes examples and test computations, and a bibliography with more than 2000 references.

Synopsis:

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.

Illustrations:

8 Illustrations, color; 103 Illustrations, black and white; XXI, 1016 p.

Publication:

Germany

Imprint:

Springer-Verlag Berlin and Heidelberg GmbH & Co. K

Returns:

Returnable

Some other items by this author:

ALGEBRAIC APPLICATIONS OF PHOTOGRAMMETRY, REMOTE SENSING AND COMPUTER VISION (HB)

ALGEBRAIC GEODESY AND GEOINFORMATICS

ALGEBRAIC GEODESY AND GEOINFORMATICS (PB)