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Keywords:
Helmert transformation; linear regression model; nonlinearity measures; weak nonlinearity
Helmert transformation; linear regression model; nonlinearity measures; weak nonlinearity
Summary:
Nowadays, the algorithm most frequently used for determination of the estimators of parameters which define a transformation between two coordinate systems (in this case the Helmert transformation) is derived under one unreal assumption of errorless measurement in the first system. As it is practically impossible to ensure errorless measurements, we can hardly believe that the results of this algorithm are “optimal”. In 1998, Kubáček and Kubáčková proposed an algorithm which takes errors in both systems into consideration. It seems to be closer to reality and at least in this sense better. However, a partial disadvantage of this algorithm is the necessity of linearization of the model which describes the problem of the given transformation. The defence of this simplification especially with respect to the bias of linear functions of the final estimators, or better to say the specification of conditions under which such a modification is statistically insignificant is the aim of this paper.
References:
[1] L. Kubáček, L. Kubáčková: Regression models with a weak nonlinearity. Preprint of the Department of Mathematical Analysis and Applied Mathematics, Faculty of Science, Palacký University, 1998. MR 1843367
[2] L. Kubáček, L. Kubáčková: Testing statistical hypotheses in deformation measurement; One generalization of the Scheffé theorem. Acta Univ. Palacki Olomuc., Fac. rer. nat., Mathematica 37 (1998), 81–88. MR 1690476
[3] J. Ševčík: Generalization of the orthogonal regression on the case of the Helmert transformation. WDS ’99 Proceedings of Contributed Papers, part I, MATFYZPRESS, Praha, 1999.
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