A multivariate version of Ghosh's T3-plot to detect non-multinormality

Kai-Tai Fang*, Run-Ze Li, Jia-Juan Liang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

30 Citations (Scopus)


Based on the theory of spherical distributions, a multivariate version of Ghosh (1996)'s T3-plot (MT3-plot) to detect non-multinormality is proposed. New critical bands for the MT3-plot based on a Kolmogorov-Smirnov type statistic are recommended to substitute Ghosh's critical bands in multivariate cases. Monte Carlo study on the choice of the projection directions gives the conclusion that the power of the MT3-plot based on the proposed Kolmogorov-Smirnov type statistic against severe non-multinormality is generally high regardless of high dimension if the projection direction is properly chosen. An application of the MT3-plot to two real-life data sets verifies the efficiency of the MT3 in finding evidence of non-multinormality in high-dimensional data analysis.

Original languageEnglish
Pages (from-to)371-386
Number of pages16
JournalComputational Statistics and Data Analysis
Issue number4
Publication statusPublished - 28 Oct 1998
Externally publishedYes

Scopus Subject Areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Graphical technique
  • Invariant statistics
  • Left-spherical matrix distribution
  • Spherical distribution
  • Test of multinormality


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