### 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 |
---|---|

ページ（範囲） | 1517-1536 |

ページ数 | 20 |

ジャーナル | Annals of Statistics |

巻 | 31 |

発行部数 | 5 |

DOI | |

出版物ステータス | 出版済み - 10 1 2003 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

### これを引用

*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.

研究成果: ジャーナルへの寄稿 › 記事

*Annals of Statistics*, 巻. 31, 番号 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 -