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Geometric aspects of robust testing for normality and sphericity
Stochastic Robustness of Control Systems under random excitation motivates challenging developments in geometric approach to robustness. The assumption of normality is rarely met when analyzing real data and thus the use of classic parametric methods with violated assumptions can result in the inacc...
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| Main Authors: | , , , |
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| Format: | Default Article |
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2017
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| Online Access: | https://hdl.handle.net/2134/23634 |
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| _version_ | 1818171492498669568 |
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| author | Wolf-Dieter Richter Lubos Strelec Hamid Abban Milan Stehlik |
| author_facet | Wolf-Dieter Richter Lubos Strelec Hamid Abban Milan Stehlik |
| author_sort | Wolf-Dieter Richter (7161593) |
| collection | Figshare |
| description | Stochastic Robustness of Control Systems under random excitation motivates challenging developments in geometric approach to robustness. The assumption of normality is rarely met when analyzing real data and thus the use of classic parametric methods with violated assumptions can result in the inaccurate computation of pvalues, e↵ect sizes, and confidence intervals. Therefore, quite naturally, research on robust testing for normality has become a new trend. Robust testing for normality can have counter-intuitive behavior, some of the problems have been introduced in [46]. Here we concentrate on explanation of small-sample e↵ects of normality testing and its robust properties, and embedding these questions into the more general question of testing for sphericity. We give geometric explanations for the critical tests. It turns out that the tests are robust against changes of the density generating function within the class of all continuous spherical sample distributions. |
| format | Default Article |
| id | rr-article-9386357 |
| institution | Loughborough University |
| publishDate | 2017 |
| record_format | Figshare |
| spelling | rr-article-93863572017-02-06T00:00:00Z Geometric aspects of robust testing for normality and sphericity Wolf-Dieter Richter (7161593) Lubos Strelec (7161596) Hamid Abban (2797075) Milan Stehlik (7161599) Statistics not elsewhere classified Other mathematical sciences not elsewhere classified Huberization Trimming Lehman-Bickel functional Monte Carlo simulations Power comparison Robust tests for normality Normality Sphericity Statistics Mathematical Sciences not elsewhere classified Stochastic Robustness of Control Systems under random excitation motivates challenging developments in geometric approach to robustness. The assumption of normality is rarely met when analyzing real data and thus the use of classic parametric methods with violated assumptions can result in the inaccurate computation of pvalues, e↵ect sizes, and confidence intervals. Therefore, quite naturally, research on robust testing for normality has become a new trend. Robust testing for normality can have counter-intuitive behavior, some of the problems have been introduced in [46]. Here we concentrate on explanation of small-sample e↵ects of normality testing and its robust properties, and embedding these questions into the more general question of testing for sphericity. We give geometric explanations for the critical tests. It turns out that the tests are robust against changes of the density generating function within the class of all continuous spherical sample distributions. 2017-02-06T00:00:00Z Text Journal contribution 2134/23634 https://figshare.com/articles/journal_contribution/Geometric_aspects_of_robust_testing_for_normality_and_sphericity/9386357 CC BY-NC-ND 4.0 |
| spellingShingle | Statistics not elsewhere classified Other mathematical sciences not elsewhere classified Huberization Trimming Lehman-Bickel functional Monte Carlo simulations Power comparison Robust tests for normality Normality Sphericity Statistics Mathematical Sciences not elsewhere classified Wolf-Dieter Richter Lubos Strelec Hamid Abban Milan Stehlik Geometric aspects of robust testing for normality and sphericity |
| title | Geometric aspects of robust testing for normality and sphericity |
| title_full | Geometric aspects of robust testing for normality and sphericity |
| title_fullStr | Geometric aspects of robust testing for normality and sphericity |
| title_full_unstemmed | Geometric aspects of robust testing for normality and sphericity |
| title_short | Geometric aspects of robust testing for normality and sphericity |
| title_sort | geometric aspects of robust testing for normality and sphericity |
| topic | Statistics not elsewhere classified Other mathematical sciences not elsewhere classified Huberization Trimming Lehman-Bickel functional Monte Carlo simulations Power comparison Robust tests for normality Normality Sphericity Statistics Mathematical Sciences not elsewhere classified |
| url | https://hdl.handle.net/2134/23634 |