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In dem vorliegenden Buch wird die Ausgleichung nach dem Total-Least-Squares-Prinzip vorgestellt und auf geodätische Problemstellungen angewandt. Total Least Squares ist ein relativ junges Verfahren im Bereich der Parameterschätzung.Für Geodäten stellt sich die Frage, ob sich Total Least Squares auch bei gängigen Problemstellungen der Geodäsie verwenden lässt und ob sich durch die Ausgleichung nach Total Least Squares im Vergleich zu den traditionellen Verfahren neue Erkenntnisse gewinnen lassen. Um die Arbeitsweise dieses Schätzers nachvollziehen zu können, werden zunächst genau die mathematischen Grundlagen vorgestellt, die in diesem Kontext eine Rolle spielen. Auf Basis dieser Grundlagen wird sowohl die klassische Berechnung einer Ausgleichung nach TLS als auch die eines gemischten TLS-LS-Problems erklärt. Weiterhin wird aufgezeigt, wie ein TLS-Problem in ein Gauß-Helmert-Problem umgewandelt werden kann, um den Kreis der möglichen Anwendungen zu erweitern. Eine kurze Zusammenfassung der wichtigsten konventionellen Modelle erleichtert die Einordnung von TLS, die auch die Entwicklung des mehrdimensionalen Beobachtungstests für Gauß-Helmert-Modelle beinhaltet. An unterschiedlichen Fallbeispielen wird untersucht, wie die Voraussetzungen für die Anwendung von TLS geschaffen werden können und welche Vorteile sich durch die Ausgleichung nach TLS ergeben.

Parameter estimation.

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This paper considers the effect of aggregation on the variance of parameter estimates for a linear regression model with random coefficients and an additive error term. Aggregate and microvariances are compared and measures of relative efficiency are introduced. Necessary conditions for efficient aggregation procedures are obtained from the Theil aggregation weights and from measures of synchronization related to the work of Grunfeld and Griliches.

Parameter estimation.

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The agrarian unrest in the United States at the end of the nineteenth century is examined. This unrest is often viewed as stemming from the inability of farmers to adapt to changing conditions in world agriculture. This hypothesis is tested in the context of a distributed lag supply function. Varying parameter estimation methods are used to trace the history of the parameters in the supply function and to decompose observed prices into permanent and transitory components over time. The patterns of variation are tested for conformity with a model of rational price-expectation formation. The conclusion is that farmers behaved as economic theory would predict, but that neither theory nor practice gave them relief from the troubles which plagued them.

Parameter estimation.

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In some applications of the distributed lag model, theory requires that all lag coefficients have a positive sign. A distributed lag estimator which provides estimated coefficients with positive sign is developed here which is analogous to an earlier distributed lag estimator derived from "smoothness priors" which did not assure that all estimated coefficients be positive. The earlier estimator with unconstrained signs was a posterior mode of the coefficients based on a spherically normal "smoothness prior" in the d+l order differences of the coefficients. The newer estimator with constrained sign is a posterior mode of the logs of the coefficients based on spherically normal "smoothness prior" on the d+l order differences of the logs of the coefficients. The meaning of both categories of prior is discussed in this paper and they are compared to prior parameterizations of the lag curve. Both varieties of "smoothness prior", in contrast to the parameterizations, allow the coefficients to assume any "smooth" shape subject to the sign constraint. The sign-constrained estimator has the additional advantage that it easily forms asymptotes. Moreover, the sign con-strained estimator is easily implemented. The estimate can be obtained by an iterative procedure involving regressions with dummy observations similar to those used to find the unconstrained sign estimator. An illustrative example of the application of both estimators is given at the end of the paper.

Estimation theory. --- Parameter estimation.

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As a byproduct of historical development, there are different, unrelated systems of nomenclature for ""inorganic chemistry"", ""organic chemistry"", ""polymer chemistry"", ""natural products chemistry"", etc. With each new discovery in the laboratory, as well as each new theoretical proposal for a chemical, the lines that traditionally have separated these ""distinct"" subsets of matter continually grow more blurred. This lack of uniformity in characterizing and naming chemicals increases the communication difficulties between differently trained chemists, as well as other scientists, and gr

Chemistry --- Parameter estimation --- System identification --- System identification. --- Parameter estimation.