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Biometrika 1980 67(2):429-439; doi:10.1093/biomet/67.2.429
© 1980 by Biometrika Trust
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A test of a multivariate normal mean with composite hypotheses determined by linear inequalities

S. SASABUCHI

Department of Mathematics, Kyushu University, Fukuoka, Japan

In this paper we propose a new multivariate generalization of a one-sided test in a way-different from that of Kud⊚ (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.

Key Words: Convex polyhedral cone • Likelihood ratio test • Linear inequalities • Multivariate normal distribution • Order restriction.


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