Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations
In geodesy, hypothesis testing is applied to a wide area of applications e.g. outlier detection, deformation analysis or, more generally, model optimisation. Due to the possible far-reaching consequences of a decision, high statistical test power of such a hypothesis test is needed. The Neyman-Pears...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-11-01
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| Series: | Journal of Geodetic Science |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/jogs-2018-0009 |
| _version_ | 1818002388673363968 |
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| author | Lehmann R. Lösler M. |
| author_facet | Lehmann R. Lösler M. |
| author_sort | Lehmann R. |
| collection | DOAJ |
| description | In geodesy, hypothesis testing is applied to a wide area of applications e.g. outlier detection, deformation analysis or, more generally, model optimisation. Due to the possible far-reaching consequences of a decision, high statistical test power of such a hypothesis test is needed. The Neyman-Pearson lemma states that under strict assumptions the often-applied likelihood ratio test has highest statistical test power and may thus fulfill the requirement. The application, however, is made more difficult as most of the decision problems are non-linear and, thus, the probability density function of the parameters does not belong to the well-known set of statistical test distributions. Moreover, the statistical test power may change, if linear approximations of the likelihood ratio test are applied. The influence of the non-linearity on hypothesis testing is investigated and exemplified by the planar coordinate transformations. Whereas several mathematical equivalent expressions are conceivable to evaluate the rotation parameter of the transformation, the decisions and, thus, the probabilities of type 1 and 2 decision errors of the related hypothesis testing are unequal to each other. Based on Monte Carlo integration, the effective decision errors are estimated and used as a basis of valuation for linear and non-linear equivalents. |
| first_indexed | 2024-04-14T03:45:18Z |
| format | Article |
| id | doaj.art-93ce6a0e6f674744bfaf7e8e29f759e6 |
| institution | Directory Open Access Journal |
| issn | 2081-9943 |
| language | English |
| last_indexed | 2024-04-14T03:45:18Z |
| publishDate | 2018-11-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Journal of Geodetic Science |
| spelling | doaj.art-93ce6a0e6f674744bfaf7e8e29f759e62022-12-22T02:14:18ZengDe GruyterJournal of Geodetic Science2081-99432018-11-01819811410.1515/jogs-2018-0009jogs-2018-0009Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate TransformationsLehmann R.0Lösler M.1University of Applied Sciences Dresden, Faculty of Spatial Information ,Dresden, GermanyFrankfurt University of Applied Sciences, Faculty of Architecture, Civil Engineering and Geomatics,Frankfurt, GermanyIn geodesy, hypothesis testing is applied to a wide area of applications e.g. outlier detection, deformation analysis or, more generally, model optimisation. Due to the possible far-reaching consequences of a decision, high statistical test power of such a hypothesis test is needed. The Neyman-Pearson lemma states that under strict assumptions the often-applied likelihood ratio test has highest statistical test power and may thus fulfill the requirement. The application, however, is made more difficult as most of the decision problems are non-linear and, thus, the probability density function of the parameters does not belong to the well-known set of statistical test distributions. Moreover, the statistical test power may change, if linear approximations of the likelihood ratio test are applied. The influence of the non-linearity on hypothesis testing is investigated and exemplified by the planar coordinate transformations. Whereas several mathematical equivalent expressions are conceivable to evaluate the rotation parameter of the transformation, the decisions and, thus, the probabilities of type 1 and 2 decision errors of the related hypothesis testing are unequal to each other. Based on Monte Carlo integration, the effective decision errors are estimated and used as a basis of valuation for linear and non-linear equivalents.https://doi.org/10.1515/jogs-2018-0009hypothesis testinglikelihood ratio test;monte carlo integrationnon-linear modelcoordinate transformation |
| spellingShingle | Lehmann R. Lösler M. Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations Journal of Geodetic Science hypothesis testing likelihood ratio test;monte carlo integration non-linear model coordinate transformation |
| title | Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations |
| title_full | Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations |
| title_fullStr | Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations |
| title_full_unstemmed | Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations |
| title_short | Hypothesis Testing in Non-Linear Models Exemplified by the Planar Coordinate Transformations |
| title_sort | hypothesis testing in non linear models exemplified by the planar coordinate transformations |
| topic | hypothesis testing likelihood ratio test;monte carlo integration non-linear model coordinate transformation |
| url | https://doi.org/10.1515/jogs-2018-0009 |
| work_keys_str_mv | AT lehmannr hypothesistestinginnonlinearmodelsexemplifiedbytheplanarcoordinatetransformations AT loslerm hypothesistestinginnonlinearmodelsexemplifiedbytheplanarcoordinatetransformations |