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20140310152330.0 |
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140214s2012 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783642222412 |
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978-3-642-22241-2 |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QC801-809 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
550 |
| Edition number |
23 |
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| Classification number |
526.1 |
| Edition number |
23 |
| 264 #1 - |
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| -- |
Berlin, Heidelberg : |
| -- |
Springer Berlin Heidelberg : |
| -- |
Imprint: Springer, |
| -- |
2012. |
| 912 ## - |
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| -- |
ZDB-2-EES |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Grafarend, Erik. |
| Relator term |
author. |
| 245 10 - IMMEDIATE SOURCE OF ACQUISITION NOTE |
|---|
| Title |
Linear and Nonlinear Models |
| Medium |
[electronic resource] : |
| Remainder of title |
Fixed effects, random effects, and total least squares / |
| Statement of responsibility, etc |
by Erik Grafarend, Joseph Awange. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XXI, 1016 p. 111 illus., 8 illus. in color. |
| Other physical details |
online resource. |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
The first problem of algebraic regression -- The first problem of algebraic regression: the bias problem Special Gauss-Markov model with datum defects, LUMBE -- 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 -- The third problem of algebraic regression -- The third problem of probabilistic regression Special Gauss-Markov model without datum defect -- Overdetermined system of nonlinear equations on curved manifolds inconsistent system of directional observational equations -- The fourth problem of probabilistic regression Special Gauss-Markov model with random effects -- Appendix A-D -- References -- Index. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc |
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 attached in a CD. 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name as entry element |
Geography. |
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| Topical term or geographic name as entry element |
Physical geography. |
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| Topical term or geographic name as entry element |
Matrix theory. |
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| Topical term or geographic name as entry element |
Mathematical statistics. |
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| Topical term or geographic name as entry element |
Earth Sciences. |
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| Topical term or geographic name as entry element |
Geophysics/Geodesy. |
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| Topical term or geographic name as entry element |
Linear and Multilinear Algebras, Matrix Theory. |
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| Topical term or geographic name as entry element |
Statistical Theory and Methods. |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Awange, Joseph. |
| Relator term |
author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
|---|
| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
|---|
| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Display text |
Printed edition: |
| International Standard Book Number |
9783642222405 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-3-642-22241-2 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
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| Item type |
E-Book |
