On optimal tests for rotational symmetry against new classes of hyperspherical distributions
E. García-Portugués, D. Paindaveine, T. Verdebout
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.
Palabras clave / Keywords: directional statistics, hypothesis testing, semiparametric statistics
Programado
Sesión J03 Estadística No Paramétrica
31 de mayo de 2018 10:20
Sala 2
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