On optimal tests for rotational symmetry against new classes of hyperspherical distributions

Eduardo Garcia-Portugues, Davy Paindaveine and Thomas Verdebout
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Eduardo Garcia-Portugues: Carlos III University of Madrid
Davy Paindaveine: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Thomas Verdebout: ECARES - European Center for Advanced Research in Economics and Statistics - ULB - Université libre de Bruxelles

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Abstract: Motivated by the central role played by rotationally symmetric distributions in directionalstatistics, we consider the problem of testing rotational symmetry on the hypersphere. We adopta semiparametric approach and tackle problems where the location of the symmetry axis iseither specified or unspecified. For each problem, we define two tests and study their asymptoticproperties under very mild conditions. We introduce two new classes of directional distributionsthat extend the rotationally symmetric class and are of independent interest. We prove thateach test is locally asymptotically maximin, in the Le Cam sense, for one kind of the alternativesgiven by the new classes of distributions, both for specified and unspecified symmetry axis. Thetests, aimed to detect location-like and scatter-like alternatives, are combined into convenienthybrid tests that are consistent against both alternatives. We perform Monte Carlo experimentsthat illustrate the finite-sample performances of the proposed tests and their agreement withthe asymptotic results. Finally, the practical relevance of our tests is illustrated on a real dataapplication from astronomy. The R packagerotasymimplements the proposed tests and allowspractitioners to reproduce the data application

Keywords: Directional data; Hypothesis testing; Local asymptotic normality; Locally asymptotically maximin tests; Rotational symmetry (search for similar items in EconPapers)
Date: 2020-09-21
New Economics Papers: this item is included in nep-ecm
Note: View the original document on HAL open archive server: https://hal.science/hal-03169388v1
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Citations: View citations in EconPapers (6)

Published in Journal of the American Statistical Association, 2020, 115 (532), pp.1873-1887. ⟨10.1080/01621459.2019.1665527⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-03169388

DOI: 10.1080/01621459.2019.1665527

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