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.
Publié le : 2003-10-14
Classification:
Common but unknown covariance matrices,
multivariate isotonic regression,
multivariate normal distribution,
order restriction,
testing homogeneity of mean vectors,
upper tail probability,
62F30,
62F03,
62H12
@article{1065705117,
author = {Sasabushi, Shoichi and Tanaka, Koji and Tsukamoto, Takeshi},
title = {Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown},
journal = {Ann. Statist.},
volume = {31},
number = {1},
year = {2003},
pages = { 1517-1536},
language = {en},
url = {http://dml.mathdoc.fr/item/1065705117}
}
Sasabushi, Shoichi; Tanaka, Koji; Tsukamoto, Takeshi. Testing homogeneity of multivariate normal mean vectors under an order restriction when the covariance matrices are common but unknown. Ann. Statist., Tome 31 (2003) no. 1, pp. 1517-1536. http://gdmltest.u-ga.fr/item/1065705117/