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

Shoichi Sasabuchi, Koji Tanaka, Takeshi Tsukamoto

22 引用 (Scopus)

### 抄録

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.

元の言語 英語 1517-1536 20 Annals of Statistics 31 5 https://doi.org/10.1214/aos/1065705117 出版済み - 10 1 2003

### Fingerprint

Order Restriction
Multivariate Normal
Homogeneity
Covariance matrix
Unknown
Testing
Tail Probability
Null hypothesis
Test Statistic
Critical point
Restriction
Estimate
Test statistic
Tail probability

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Statistics, Probability and Uncertainty

### これを引用

Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. / Sasabuchi, Shoichi; Tanaka, Koji; Tsukamoto, Takeshi.

：: Annals of Statistics, 巻 31, 番号 5, 01.10.2003, p. 1517-1536.

Sasabuchi, Shoichi ; Tanaka, Koji ; Tsukamoto, Takeshi. / Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. ：: Annals of Statistics. 2003 ; 巻 31, 番号 5. pp. 1517-1536.
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