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Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. (English) Zbl 1065.62111

Summary: Suppose that an order restriction is imposed among several \(p\)-variate normal mean vectors. We are interested in testing the homogeneity of these mean vectors under this restriction. This problem is a multivariate extension of S. Bartholomew’s [Biometrika 46, 36–48 (1959; Zbl 0087.14202)] method. When the covariance matrices are known, this problem has been studied by S. Sasabuchi, M. Inutsuka and D. D. S. Kulatunga [Hiroshima Math. J. 22, 551–560 (1992; Zbl 0765.62069)], S. Sasabuchi, D. D. S. Kulatunga and H. Saito [Am. J. Math. Manage Sci. 18, 131–158 (1998; Zbl 0919.62055)], and some others.
We consider the case when the covariance matrices are common but unknown. We propose a test statistic, study its upper tail probability under the null hypothesis and estimate its critical points.

MSC:

62H15 Hypothesis testing in multivariate analysis
62F30 Parametric inference under constraints
62F03 Parametric hypothesis testing
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References:

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