### Abstract

Suppose that an order restriction is imposed among several p-variate normal mean vectors. We are interested in the problems of estimating these mean vectors and testing their homogeneity under this restriction. These problems are multivariate extensions of Bartholomew's (1959) ones. For the bivariate case, these problems have been studied by Sasabuchi et al. (1983) and (1998) and some others. In the present paper we examine the convergence of an iterative algorithm for computing the maximum likelihood estimator when p is larger than two, We also study some test procedures for testing homogeneity when p is larger than two.

Original language | English |
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Pages (from-to) | 619-641 |

Number of pages | 23 |

Journal | Journal of Statistical Computation and Simulation |

Volume | 73 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 1 2003 |

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### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Modelling and Simulation
- Statistics, Probability and Uncertainty
- Applied Mathematics

### Cite this

*Journal of Statistical Computation and Simulation*,

*73*(9), 619-641. https://doi.org/10.1080/0094965021000044420

**Estimation and test of several multivariate normal means under an order restriction when the dimension is larger than two.** / Sasabuchi, Shoichi; Miura, Takashi; Oda, Hitoshi.

Research output: Contribution to journal › Article

*Journal of Statistical Computation and Simulation*, vol. 73, no. 9, pp. 619-641. https://doi.org/10.1080/0094965021000044420

}

TY - JOUR

T1 - Estimation and test of several multivariate normal means under an order restriction when the dimension is larger than two

AU - Sasabuchi, Shoichi

AU - Miura, Takashi

AU - Oda, Hitoshi

PY - 2003/9/1

Y1 - 2003/9/1

N2 - Suppose that an order restriction is imposed among several p-variate normal mean vectors. We are interested in the problems of estimating these mean vectors and testing their homogeneity under this restriction. These problems are multivariate extensions of Bartholomew's (1959) ones. For the bivariate case, these problems have been studied by Sasabuchi et al. (1983) and (1998) and some others. In the present paper we examine the convergence of an iterative algorithm for computing the maximum likelihood estimator when p is larger than two, We also study some test procedures for testing homogeneity when p is larger than two.

AB - Suppose that an order restriction is imposed among several p-variate normal mean vectors. We are interested in the problems of estimating these mean vectors and testing their homogeneity under this restriction. These problems are multivariate extensions of Bartholomew's (1959) ones. For the bivariate case, these problems have been studied by Sasabuchi et al. (1983) and (1998) and some others. In the present paper we examine the convergence of an iterative algorithm for computing the maximum likelihood estimator when p is larger than two, We also study some test procedures for testing homogeneity when p is larger than two.

UR - http://www.scopus.com/inward/record.url?scp=0041417512&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041417512&partnerID=8YFLogxK

U2 - 10.1080/0094965021000044420

DO - 10.1080/0094965021000044420

M3 - Article

VL - 73

SP - 619

EP - 641

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

SN - 0094-9655

IS - 9

ER -