Testing multivariate symmetry

C. R. Heathcote, S. T. Rachev, B. Cheng

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


The paper presents a procedure for testing a general multivariate distribution for symmetry about a point and, also, a procedure adapted to the special properties of multivariate stable laws. In the general case use is made of a stochastic process derived from the empirical characteristic function. Under symmetry weak convergence to a Gaussian process is established and a test statistic is defined in terms of this limit process. Unlike circumstances in the univariate case, it is found convenient to estimate the center of symmetry and a spherically trimmed mean is used for that purpose. The procedure specifically concerned with multivariate stable laws is based on estimates of the spectral measure and index of stability. A numerical example concerning a bivariate distribution is given.

Original languageEnglish
Pages (from-to)91-112
Number of pages22
JournalJournal of Multivariate Analysis
Issue number1
StatePublished - Jul 1995


  • Center of symmetry
  • Empirical characteristic function
  • Multivariate stable laws
  • Multivariate symmetry


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