###
A PROCEDURE FOR ASSESSING VECTOR CORRELATIONS

###
JÉRÔME ALLAIRE AND YVES LEPAGE

*Département de mathématiques et de statistique,*

Université de Montréal, Montréal, Québec, Canada H3C 3J7
(Received November 21, 1990; revised November 20, 1991)

**Abstract.**
Three known measures of multivariate relationship are
presented. Under the null hypothesis of lack of multivariate relationship
between
*K* random vectors, the asymptotic joint distributions of the
\displaystyle{K\choose 2} values taken by these measures for all possible
pairs
(*X*^{(i)},*X*^{(j)}), 1 __<__ i < j __<__ *K*, is used to construct tests of the null
hypothesis based on the maximum and more generally, on the greatest values
of the
measures. The asymptotic power of the tests is also obtained under a sequence of
alternatives.

*Key words and phrases*:
Multivariate relationship, matrix
correlation,
asymptotic distributions, elliptical distributions, hypothesis testing.

**Source**
( TeX ,
DVI ,
PS )