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

Shoichi Sasabuchi, Koji Tanaka, Takeshi Tsukamoto

Research output: Contribution to journalArticle

22 Citations (Scopus)

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 languageEnglish
Pages (from-to)1517-1536
Number of pages20
JournalAnnals of Statistics
Volume31
Issue number5
DOIs
Publication statusPublished - Oct 1 2003

Fingerprint

Order Restriction
Multivariate Normal
Homogeneity
Covariance matrix
Unknown
Testing
Tail Probability
Null hypothesis
Test Statistic
Critical point
Restriction
Estimate
Test statistic
Tail probability

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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.

In: Annals of Statistics, Vol. 31, No. 5, 01.10.2003, p. 1517-1536.

Research output: Contribution to journalArticle

Sasabuchi, Shoichi ; Tanaka, Koji ; Tsukamoto, Takeshi. / Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. In: Annals of Statistics. 2003 ; Vol. 31, No. 5. pp. 1517-1536.
@article{5676da4276494d1ea675a37e44df31b8,
title = "Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown",
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.",
author = "Shoichi Sasabuchi and Koji Tanaka and Takeshi Tsukamoto",
year = "2003",
month = "10",
day = "1",
doi = "10.1214/aos/1065705117",
language = "English",
volume = "31",
pages = "1517--1536",
journal = "Annals of Statistics",
issn = "0090-5364",
publisher = "Institute of Mathematical Statistics",
number = "5",

}

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 -