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

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    23 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 2003

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Statistics, Probability and Uncertainty

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