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Skew-rotationally-symmetric distributions and related efficient inferential procedures

Christophe Ley and Thomas Verdebout

Journal of Multivariate Analysis, 2017, vol. 159, issue C, 67-81

Abstract: Most commonly used distributions on the unit hypersphere Sk−1={v∈Rk:v⊤v=1}, k≥2, assume that the data are rotationally symmetric about some direction θ∈Sk−1. 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 Sk−1 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.

Keywords: Directional statistics; Rotationally symmetric distributions; Skew-symmetric distributions; Tests for rotational symmetry (search for similar items in EconPapers)
Date: 2017
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