Permutation Tests for Reflected Symmetry

Georg Neuhaus, Lixing ZHU

Research output: Contribution to journalJournal articlepeer-review

30 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)129-153
Number of pages25
JournalJournal of Multivariate Analysis
Issue number2
Publication statusPublished - Nov 1998

Scopus Subject Areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

User-Defined Keywords

  • Empirical characteristic function, empirical process, permutation tests, reflected symmetry, validity of test


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