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Permutation Tests for Reflected Symmetry

✍ Scribed by Georg Neuhaus; Li-Xing Zhu

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
360 KB
Volume
67
Category
Article
ISSN
0047-259X

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✦ Synopsis

The paper presents a permutation procedure for testing reflected (or diagonal) symmetry of the distribution of a multivariate variable. The test statistics are based in empirical characteristic functions. The resulting permutation tests are strictly distribution free under the null hypothesis that the underlying variables are symmetrically distributed about a center. Furthermore, the permutation tests are strictly valid if the symmetric center is known and are asymptotic valid if the center is an unknown point. The equivalence, in the large sample sense, between the tests and their permutation counterparts are established. The power behavior of the tests and their permutation counterparts under local alternative are investigated. Some simulations with small sample sizes ( 20) are conducted to demonstrate how the permutation tests works.

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