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

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Authors Eduardo Garc'ia-Portugu'es, Davy Paindaveine, Thomas Verdebout
Journal/Conference Name arXiv
Paper Category
Paper Abstract 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 the situations 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, both for specified and unspecified symmetry axis. The tests, aimed to detect location-like and scatter-like alternatives, are combined into a convenient hybrid test that is consistent against both alternatives. A Monte Carlo study illustrates the finite-sample performances of the tests and corroborates empirically the theoretical findings. Finally, we apply the tests for assessing rotational symmetry in two real data examples coming from geology and proteomics.
Date of publication 2017
Code Programming Language R

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