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

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 |

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty

## Fingerprint Dive into the research topics of 'Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown'. Together they form a unique fingerprint.

## Cite this

*Annals of Statistics*,

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