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
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X17301227
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:159:y:2017:i:c:p:67-81

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2017.02.010

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().