Geometric aspects of robust testing for normality and sphericity |
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Authors: | Wolf-Dieter Richter Luboš Střelec Hamid Ahmadinezhad |
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Institution: | 1. Institute of Mathematics, University of Rostock, Rostock, Germany;2. Department of Statistics and Operation Analysis, Mendel University in Brno, Brno, Czech Republic;3. Department of Mathematical Sciences, Loughborough University, Loughborough, UK |
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Abstract: | 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 p-values, effect sizes, and confidence intervals. Therefore, quite naturally, research on robust testing for normality has become a new trend. Robust testing for normality can have counterintuitive behavior, some of the problems have been introduced in Stehlík et al. Chemometrics and Intelligent Laboratory Systems 130 (2014 Stehlík, M., St?elec, L., and Thulin, M. 2014. On robust testing for normality in chemometrics. Chemometrics and Intelligent Laboratory Systems 130:98–108.Crossref], Web of Science ®] , Google Scholar]): 98–108]. Here we concentrate on explanation of small-sample effects 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. |
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Keywords: | Huberization trimming Lehmann–Bickel functional Monte Carlo simulations power comparison robust tests for normality normality sphericity |
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