Applications of linear and nonlinear models :
- 出版日期：c2012.
- 出版者：Springer,
- 页数：xxi, 1016 p. :
- 出版地：Berlin :
- 第一责任说明：Erik W. Grafarend, Joseph L. Awange.
- 尺寸：25 cm.
- 分类号：a116
- ISBN：978-3-642-22240-5(hdk.) :
MARC全文
02h0026352 20150304195854.0 121226s2012 gw a frb |001|||eng | 978-3-642-22240-5(hdk.) : CNY1494.00 NGL NGL NGL 519.5/36 23 a116 Grafarend, Erik W. Applications of linear and nonlinear models : fixed effects, random effects, and total least squares / Erik W. Grafarend, Joseph L. Awange. Berlin : Springer, c2012. xxi, 1016 p. : ill. (some col.) ; 25 cm. Springer geophysics Includes bibliographic reference and index. Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear egression 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 aGauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a tochastic 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 stimators/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. Regression analysis. ; Mathematical statistics. ; Probabilities. ; Nonlinear theories. aAwange, Joseph L., ; d1969- Springer geophysics. aCN b010001 NGL 116 G75 gljx1204 h1 ; rCNY1494.00