文章基本信息

标题：A GENERALIZATION OF TESTING INDEPENDENCE OF SETS OF VARIATES
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作者：Akio Suzukawa ; Yoshiharu Sato
期刊名称：JOURNAL OF THE JAPAN STATISTICAL SOCIETY
印刷版ISSN：1882-2754
电子版ISSN：1348-6365
出版年度：1995
卷号：25
期号：1
页码：71-80
DOI：10.14490/jjss1995.25.71
出版社：JAPAN STATISTICAL SOCIETY
摘要：Assuming that X =( X ⁽¹⁾', X ⁽²⁾', …, X ^(q)')' is distributed according to N_p (μ, Σ) and each X^(j) has p_j components, where p = p ₁+…+ p_q and p ₁≥ p ₂≥…≥ p_q , we consider the testing of the hypothesis that for a =2, …, q , all the smallest p_a - k_a canonical correlations between ( X ⁽¹⁾', X ⁽²⁾', …, X ^{( a -1)}')' and X ^{( a )} are zero. In the case of k ₂= k ₃=…= k_q =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.