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.


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