The effects on the distributions of sample canonical correlations under nonnormality

Takashi Seo, Yasunori Fujikoshi, Takashi Kanda

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In this paper, we study the effects of nonnormality on the distributions of sample canonical correlations when the population canonical correlations are simple. In order to achieve the purpose, we derive asymptotic expansion formulas for the distributions of a function of the canonical correlations as well as the individual canonical correlations under nonnormal populations. We particularly discuss the distribution of sample canonical correlations under the class of elliptical population. These expansions are given by using a perturbation method. Simulation results are also given.

Original languageEnglish
Pages (from-to)2615-2628
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Issue number9
Publication statusPublished - 1 Jan 1994



  • asymptotic expansion
  • canonical correlation
  • elliptical distribution
  • nonnormal population

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