## The Annals of Statistics

### Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown

#### 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.

#### Article information

Source
Ann. Statist., Volume 31, Number 5 (2003), 1517-1536.

Dates
First available in Project Euclid: 9 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1065705117

Digital Object Identifier
doi:10.1214/aos/1065705117

Mathematical Reviews number (MathSciNet)
MR2012824

Zentralblatt MATH identifier
1065.62111

Subjects
Primary: 62F30: Inference under constraints
Secondary: 62F03: Hypothesis testing 62H12: Estimation

#### Citation

Sasabushi, Shoichi; Tanaka, Koji; Tsukamoto, Takeshi. Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. Ann. Statist. 31 (2003), no. 5, 1517--1536. doi:10.1214/aos/1065705117. https://projecteuclid.org/euclid.aos/1065705117

#### References

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