Linear and nonlinear models: fixed effects, random effects, and total least squares

Here we present a nearly complete treatment of the 'Grand Universe' of linearand weakly nonlinear regression models within the first 8 chapters. The pointof 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. The first six chapters concentrate on underdeterminedand overdetermined linear systems as well as systems with a datum defect. Also reviewed are 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 discusscontinues networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapterseven is a speciality in the treatment of an overdetermined system of nonlinear equations of curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. The final 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. Throughout we give numerous examples and present various test computations. The exhaustive bibliography includes more than 2000 references , books and papers. Numerous geodetic examples and various test computations are given. Thetreatment of both linear and nonlinear geodetic problems side by side as donein the present book is rare to come by. The polynomial methods adopting Groeber basis and resultants techniques to solve more complicated nonlinear problems are presented INDICE: 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 oflinear 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

• ISBN: 978-3-642-22240-5
• Editorial: Springer Berlin Heidelberg
• Encuadernacion: Cartoné
• Páginas: 700
• Fecha Publicación: 09/11/2011
• Nº Volúmenes: 1
• Idioma: Inglés