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.
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Acknowledgments
We are grateful to the two reviewers, whose constructive comments led to the current version of the paper. This paper is based on work carried out as part of the PhD thesis of the first author, who gratefully acknowledges the funding received by the EPSRC. We are also thankful to Dr. Dimitrios Bagkavos for bringing the Kasuya (2010) reference to our notice.
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Partlett, C., Patil, P. Measuring asymmetry and testing symmetry. Ann Inst Stat Math 69, 429–460 (2017). https://doi.org/10.1007/s10463-015-0547-4
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DOI: https://doi.org/10.1007/s10463-015-0547-4