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Title: On some tests for rotational symmetry Authors:  Thomas Verdebout - Universite Libre de Bruxelles (Belgium) [presenting]
Davy Paindaveine - Universite libre de Bruxelles (Belgium)
Eduardo Garcia-Portugues - Carlos III University of Madrid (Spain)
Abstract: Most commonly-used distributions on unit hyperspheres assume that the data are rotationally symmetric about some direction. The problem of testing for rotational symmetry has been relatively well studied in the circular case. Surprisingly, it has been quite less investigated in the spherical or hyperspherical one. We propose new tests of rotational symmetry on hyperspheres. We show that our tests enjoy many desirable properties. In particular they are locally and asymptotically optimal against new classes of distributions. Our results are illustrated via Monte-Carlo simulations and on a real data related to the study of protein structures.