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Testing symmetry around a subspace

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The article shows how some common measures of association between two random vectors may be used to test multivariate symmetry around a subspace (possibly up to a shift), which also permits testing exchangeability, axial symmetry, halfspace symmetry, and certain goodness-of-fit and equality-of-scale hypotheses. The resulting (parametric, nonparametric, permutation, and asymptotic) tests of the symmetry, consistent in the class of all elliptical distributions, are also illustrated with a few simulation and real data examples.

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The research of Miroslav Šiman was supported by the Czech Science Foundation Project GA17-07384S. He would like to thank Jana Klicnarová and Pavel Boček for IT and research assistance. The research of Šárka Hudecová was supported by the grant GA18-08888S. We also thank the editor and anonymous reviewers for their suggestions and for pointing us to Rattihalli et al. (2019).

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Correspondence to Šárka Hudecová.

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Hudecová, Š., Šiman, M. Testing symmetry around a subspace. Stat Papers 62, 2491–2508 (2021).

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