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 % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaeWaaeaafa% qabeGabaaabaGaam4saaqaaiaaikdaaaaacaGLOaGaayzkaaaaaa!390F!\[\left( {\begin{array}{*{20}c}K \\2 \\\end{array} } \right)\]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.
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The author was partially supported by a grant of the Natural Sciences and Engineering Research Council of Canada.
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Allaire, J., Lepage, Y. A procedure for assessing vector correlations. Ann Inst Stat Math 44, 755–768 (1992). https://doi.org/10.1007/BF00053404
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DOI: https://doi.org/10.1007/BF00053404