Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 115, Issue 532, Pages 1873-1887Publisher
AMER STATISTICAL ASSOC
DOI: 10.1080/01621459.2019.1665527
Keywords
Directional data; Hypothesis testing; Local asymptotic normality; Locally asymptotically maximin tests; Rotational symmetry
Categories
Funding
- Spanish Ministry of Science, Innovation and Universities [PGC2018097284-B-I00, IJCI-2017-32005, MTM2016-76969-P]
- European Regional Development Fund
- Francqui Foundation
- Program of Concerted Research Actions (ARC) of the Universite libre de Bruxelles
- ARC Program of the Universite libre de Bruxelles
- Credit de Recherche of the FNRS (Communaute Francaise de Belgique) [J.0134.18]
- National Bank of Belgium
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Motivated by the central role played by rotationally symmetric distributions in directional statistics, we consider the problem of testing rotational symmetry on the hypersphere. We adopt a semiparametric approach and tackle problems where the location of the symmetry axis is either specified or unspecified. For each problem, we define two tests and study their asymptotic properties under very mild conditions. We introduce two new classes of directional distributions that extend the rotationally symmetric class and are of independent interest. We prove that each test is locally asymptotically maximin, in the Le Cam sense, for one kind of the alternatives given by the new classes of distributions, for both specified and unspecified symmetry axis. The tests, aimed to detect location- and scatter-like alternatives, are combined into convenient hybrid tests that are consistent against both alternatives. We perform Monte Carlo experiments that illustrate the finite-sample performances of the proposed tests and their agreement with the asymptotic results. Finally, the practical relevance of our tests is illustrated on a real data application from astronomy. The R package rotasym implements the proposed tests and allows practitioners to reproduce the data application. for this article are available online.
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