### 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.

Original language | English |
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Pages (from-to) | 1517-1536 |

Number of pages | 20 |

Journal | Annals of Statistics |

Volume | 31 |

Issue number | 5 |

DOIs | |

Publication status | Published - Oct 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Annals of Statistics*,

*31*(5), 1517-1536. https://doi.org/10.1214/aos/1065705117

**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.

Research output: Contribution to journal › Article

*Annals of Statistics*, vol. 31, no. 5, pp. 1517-1536. https://doi.org/10.1214/aos/1065705117

}

TY - JOUR

T1 - Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown

AU - Sasabuchi, Shoichi

AU - Tanaka, Koji

AU - Tsukamoto, Takeshi

PY - 2003/10/1

Y1 - 2003/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0242595972&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0242595972&partnerID=8YFLogxK

U2 - 10.1214/aos/1065705117

DO - 10.1214/aos/1065705117

M3 - Article

VL - 31

SP - 1517

EP - 1536

JO - Annals of Statistics

JF - Annals of Statistics

SN - 0090-5364

IS - 5

ER -