Kargoll, Boris: On the theory and application of model misspecification tests in geodesy. - Bonn, 2007. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5N-11136
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5N-11136,
author = {{Boris Kargoll}},
title = {On the theory and application of model misspecification tests in geodesy},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2007,
note = {Many geodetic testing problems concerning parametric hypotheses may be formulated within the framework of testing linear constraints imposed on a linear Gauss-Markov model. Although geodetic standard tests for such problems are computationally convenient and intuitively sound, no rigorous attempt has yet been made to derive them from a unified theoretical foundation or to establish optimality of such procedures. Another shortcoming of current geodetic testing theory is that no standard approach exists for tackling analytically more complex testing problems, concerning for instance unknown parameters within the weight matrix.
To address these problems, it is proven that, under the assumption of normally distributed observation, various geodetic standard tests, such as Baarda's or Pope's test for outliers, multivariate significance tests, deformation tests, or tests concerning the specification of the a priori variance factor, are uniformly most powerful (UMP) within the class of invariant tests. UMP invariant tests are proven to be equivalent to likelihood ratio tests and Rao's score tests. It is also shown that the computation of many geodetic standard tests may be simplified by transforming them into Rao's score tests.
Finally, testing problems concerning unknown parameters within the weight matrix such as autoregressive correlation parameters or overlapping variance components are addressed. It is shown that, although strictly optimal tests do not exist in such cases, corresponding tests based on Rao's Score statistic are reasonable and computationally convenient diagnostic tools for deciding whether such parameters are significant or not. The thesis concludes with the derivation of a parametric test of normality as another application of Rao's Score test.},

url = {https://hdl.handle.net/20.500.11811/2723}

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