JOURNAL OF THE JAPAN STATISTICAL SOCIETY
Online ISSN : 1348-6365
Print ISSN : 1882-2754
ISSN-L : 1348-6365
A GENERALIZATION OF TESTING INDEPENDENCE OF SETS OF VARIATES
Akio SuzukawaYoshiharu Sato
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1995 年 25 巻 1 号 p. 71-80

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Assuming that X=(X(1)', X(2)', …, X(q)')' is distributed according to Np(μ, Σ) and each X(j) has pj components, where p=p1+…+pq and p1p2≥…≥pq, we consider the testing of the hypothesis that for a=2, …, q, all the smallest pa-ka canonical correlations between (X(1)', X(2)', …, X(a-1)')' and X(a) are zero. In the case of k2=k3=…=kq=0, this hypothesis is equivalent to the hypothesis of independence of X(1), X(2), …, X(q). This testing problem can then be considered to be a generalization of the problem of testing independence. In this paper we drive the likelihood ratio statistic (LR statistic) and obtain the asymptotic expansion of its null distribution. We also obtain the asymptotic expansions of the null distributions of the other two statistics, which are the statistics corresponding to Lawley-Hotelling's trace and the Bartlett-Nanda-Pillai's trace criterion.
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