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1	Transformation model selection by multiple hypotheses testing Lehmann, Rüdiger 17 October 2016 (has links) (PDF) Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide. Koordinatentransformation Hypothesentest Affintransformation Ähnlichkeitstransformation Gauß-Markow-Model mit Nebenbedingungen Normierter Lagrange-Multiplikator Studentisierter Lagrange-Multiplikator Akaike's Informationskriterium Mallows’ Cp Coordinate transformation Hypothesis test Affine transformation Similarity transformation Gauss-Markov model with constraints Normalized Lagrange multiplier Studentized Lagrange multiplier Akaike information criterion Mallows’ Cp ddc:500 rvk:ZI 9070
2	Observation error model selection by information criteria vs. normality testing Lehmann, Rüdiger 17 October 2016 (has links) (PDF) To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution we compare the Akaike information criterion (AIC) and the Anderson Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test. Maximum-Likelihood-Schätzung Robuste Schätzung Gaußsche Normalverteilung Laplace-Verteilung Verallgemeinerte Normalverteilung Kontaminierte Normalverteilung Akaike's Informationskriterium Anderson-Darling-Test Monte-Carlo-Methode maximum likelihood estimation robust estimation Gaussian normal distribution Laplace distribution generalized normal distribution contaminated normal distribution Akaike information criterion Anderson Darling test Monte Carlo method ddc:500 rvk:ZI 9070
3	Transformation model selection by multiple hypotheses testing Lehmann, Rüdiger January 2014 (has links) Transformations between different geodetic reference frames are often performed such that first the transformation parameters are determined from control points. If in the first place we do not know which of the numerous transformation models is appropriate then we can set up a multiple hypotheses test. The paper extends the common method of testing transformation parameters for significance, to the case that also constraints for such parameters are tested. This provides more flexibility when setting up such a test. One can formulate a general model with a maximum number of transformation parameters and specialize it by adding constraints to those parameters, which need to be tested. The proper test statistic in a multiple test is shown to be either the extreme normalized or the extreme studentized Lagrange multiplier. They are shown to perform superior to the more intuitive test statistics derived from misclosures. It is shown how model selection by multiple hypotheses testing relates to the use of information criteria like AICc and Mallows’ Cp, which are based on an information theoretic approach. Nevertheless, whenever comparable, the results of an exemplary computation almost coincide. info:eu-repo/classification/ddc/500 ddc:500
4	Observation error model selection by information criteria vs. normality testing Lehmann, Rüdiger January 2015 (has links) To extract the best possible information from geodetic and geophysical observations, it is necessary to select a model of the observation errors, mostly the family of Gaussian normal distributions. However, there are alternatives, typically chosen in the framework of robust M-estimation. We give a synopsis of well-known and less well-known models for observation errors and propose to select a model based on information criteria. In this contribution we compare the Akaike information criterion (AIC) and the Anderson Darling (AD) test and apply them to the test problem of fitting a straight line. The comparison is facilitated by a Monte Carlo approach. It turns out that the model selection by AIC has some advantages over the AD test. info:eu-repo/classification/ddc/500 ddc:500

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