Measuring asymmetry and testing symmetry

Partlett, Christopher; Patil, Prakash

Abstract

In this paper, we show that some of the most commonly used tests of symmetry do not have power which is reflective of the size of asymmetry. This is because the primary rationale for the test statistics that are proposed in the literature to test for symmetry is to detect the departure from symmetry, rather than the quantification of the asymmetry. As a result, tests of symmetry based upon these statistics do not necessarily generate power that is representative of the departure from the null hypothesis of symmetry. Recent research has produced new measures of asymmetry, which have been shown to do an admirable job of quantifying the amount of asymmetry. We propose several new tests based upon one such measure. We derive the asymptotic distribution of the test statistics and analyse the performance of these proposed tests through the use of a simulation study.

Citation

Partlett, C., & Patil, P. (2017). Measuring asymmetry and testing symmetry. Annals of the Institute of Statistical Mathematics, 69(2), 429-460. https://doi.org/10.1007/s10463-015-0547-4

• Journal Article Type: Article
• Acceptance Date: Dec 14, 2015
• Online Publication Date: Dec 14, 2015
• Publication Date: 2017-04
• Deposit Date: Jun 12, 2019
• Journal: Annals of the Institute of Statistical Mathematics
• Print ISSN: 0020-3157
• Electronic ISSN: 1572-9052
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 69
• Issue: 2
• Pages: 429-460
• DOI: https://doi.org/10.1007/s10463-015-0547-4
• Public URL: https://nottingham-repository.worktribe.com/output/1768685
• Publisher URL: https://link.springer.com/article/10.1007%2Fs10463-015-0547-4