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This book presents a nearly complete treatment 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. 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, the authors 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 specialty 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 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 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
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
