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

Shoichi Sasabuchi

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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

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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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