### 抄録

In this paper we propose a new multivariate generalization of a one-sided test in a way-different from that of Kud{circled ring operator} (1963). Let X be a p-variate normal random variable with the mean vector μ. and a known covariance matrix. We consider the null hypothesis that μ. lies on the boundary of a convex polyhedral cone determined by linear inequalities; the alternative is that μ lies in its interior. A two-sided version is also discussed. This paper provides likelihood ratio tests and some applications along with some discussion of the geometry of convex polyhedral cones.

元の言語 | 英語 |
---|---|

ページ（範囲） | 429-439 |

ページ数 | 11 |

ジャーナル | Biometrika |

巻 | 67 |

発行部数 | 2 |

DOI | |

出版物ステータス | 出版済み - 12 1 1980 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Mathematics(all)
- Statistics and Probability
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences(all)

### これを引用

*Biometrika*,

*67*(2), 429-439. https://doi.org/10.1093/biomet/67.2.429

**A test of a multivariate normal mean with composite hypotheses determined by linear inequalities.** / Sasabuchi, Shoichi.

研究成果: ジャーナルへの寄稿 › 記事

*Biometrika*, 巻. 67, 番号 2, pp. 429-439. https://doi.org/10.1093/biomet/67.2.429

}

TY - JOUR

T1 - A test of a multivariate normal mean with composite hypotheses determined by linear inequalities

AU - Sasabuchi, Shoichi

PY - 1980/12/1

Y1 - 1980/12/1

N2 - In this paper we propose a new multivariate generalization of a one-sided test in a way-different from that of Kud{circled ring operator} (1963). Let X be a p-variate normal random variable with the mean vector μ. and a known covariance matrix. We consider the null hypothesis that μ. lies on the boundary of a convex polyhedral cone determined by linear inequalities; the alternative is that μ lies in its interior. A two-sided version is also discussed. This paper provides likelihood ratio tests and some applications along with some discussion of the geometry of convex polyhedral cones.

AB - In this paper we propose a new multivariate generalization of a one-sided test in a way-different from that of Kud{circled ring operator} (1963). Let X be a p-variate normal random variable with the mean vector μ. and a known covariance matrix. We consider the null hypothesis that μ. lies on the boundary of a convex polyhedral cone determined by linear inequalities; the alternative is that μ lies in its interior. A two-sided version is also discussed. This paper provides likelihood ratio tests and some applications along with some discussion of the geometry of convex polyhedral cones.

UR - http://www.scopus.com/inward/record.url?scp=0001244494&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001244494&partnerID=8YFLogxK

U2 - 10.1093/biomet/67.2.429

DO - 10.1093/biomet/67.2.429

M3 - Article

VL - 67

SP - 429

EP - 439

JO - Biometrika

JF - Biometrika

SN - 0006-3444

IS - 2

ER -