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October 2003 Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown
Shoichi Sasabushi, Koji Tanaka, Takeshi Tsukamoto
Ann. Statist. 31(5): 1517-1536 (October 2003). DOI: 10.1214/aos/1065705117

Abstract

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 Bartholomew's [Biometrika} 46 (1959) 36-48]. When the covariance matrices are known, this problem has been studied by Sasabuchi, Inutsuka and Kulatunga [Hiroshima Math. J. 22 (1992) 551-560], Sasabuchi, Kulatunga and Saito [Amer. J. Math. Management Sci. 18 (1998) 131-158] and some others. In the present paper, 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.

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Shoichi Sasabushi. Koji Tanaka. Takeshi Tsukamoto. "Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown." Ann. Statist. 31 (5) 1517 - 1536, October 2003. https://doi.org/10.1214/aos/1065705117

Information

Published: October 2003
First available in Project Euclid: 9 October 2003

zbMATH: 1065.62111
MathSciNet: MR2012824
Digital Object Identifier: 10.1214/aos/1065705117

Subjects:
Primary: 62F30
Secondary: 62F03, 62H12

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 5 • October 2003
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