A necessary test of goodness of fit for sphericity

Kai Tai Fang, Lixing Zhu, Peter M. Bentler

Research output: Contribution to journalJournal articlepeer-review

26 Citations (Scopus)


A p × 1 random vector x is said to have a spherical distribution, if for every p × p orthogonal matrix Q, x and Qx have the same distribution. In this paper, some nonparametric goodness of fit Wilcoxon-type tests for sphericity are proposed. Some results on the limiting distributions of the statistics are obtained. These results provide a theoretical basis for a necessary test of sphericity.

Original languageEnglish
Pages (from-to)34-55
Number of pages22
JournalJournal of Multivariate Analysis
Issue number1
Publication statusPublished - Apr 1993

Scopus Subject Areas

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

User-Defined Keywords

  • Goodness of fit
  • Nonparametric
  • Wilcoxon statistics


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