Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5129383 | Journal of Multivariate Analysis | 2017 | 15 Pages |
Most commonly used distributions on the unit hypersphere Skâ1={vâRk:vâ¤v=1}, kâ¥2, assume that the data are rotationally symmetric about some direction θâSkâ1. However, there is empirical evidence that this assumption often fails to describe reality. We study in this paper a new class of skew-rotationally-symmetric distributions on Skâ1 that enjoy numerous good properties. We discuss the Fisher information structure of the model and derive efficient inferential procedures. In particular, we obtain the first semi-parametric test for rotational symmetry about a known direction. We also propose a second test for rotational symmetry, obtained through the definition of a new measure of skewness on the hypersphere. We investigate the finite-sample behavior of the new tests through a Monte Carlo simulation study. We conclude the paper with a discussion about some intriguing open questions related to our new models.