Applications of Linear and Nonlinear Models

by Grafarend, Erik W.; Awange, Joseph L.

• ISBN13: 9783642222405
• ISBN10: 3642222404
• Format: Hardcover
• Copyright: 2012-08-06
• Publisher: Springer Verlag

Summary

Here we present a nearly complete treatment of the 'Grand Universe' of linear and weakly nonlinear regression models within the first 8 chapters. The 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. The first six chapters concentrate on underdetermined and 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 discuss continues 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 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.