A test of a multivariate normal mean with composite hypotheses determined by linear inequalities

Shoichi Sasabuchi

    Research output: Contribution to journalArticlepeer-review

    155 Citations (Scopus)

    Abstract

    In this paper we propose a new multivariate generalization of a one-sided test in a way-different from that of Kud{circled ring operator} (1963). Let X be a p-variate normal random variable with the mean vector μ. and a known covariance matrix. We consider the null hypothesis that μ. lies on the boundary of a convex polyhedral cone determined by linear inequalities; the alternative is that μ lies in its interior. A two-sided version is also discussed. This paper provides likelihood ratio tests and some applications along with some discussion of the geometry of convex polyhedral cones.

    Original languageEnglish
    Pages (from-to)429-439
    Number of pages11
    JournalBiometrika
    Volume67
    Issue number2
    DOIs
    Publication statusPublished - Dec 1 1980

    All Science Journal Classification (ASJC) codes

    • Statistics, Probability and Uncertainty
    • Applied Mathematics
    • Mathematics(all)
    • Statistics and Probability
    • Agricultural and Biological Sciences (miscellaneous)
    • Agricultural and Biological Sciences(all)

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