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

Shoichi Sasabuchi

doi:10.1093/biomet/67.2.429

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

Shoichi Sasabuchi

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Research output: Contribution to journal › Article

98 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 language	English
Pages (from-to)	429-439
Number of pages	11
Journal	Biometrika
Volume	67
Issue number	2
DOIs	https://doi.org/10.1093/biomet/67.2.429
Publication status	Published - Dec 1 1980

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Composite Hypothesis

Polyhedral Cones

Multivariate Normal

Convex Cone

Cones

Linear Inequalities

One-sided test

Composite materials

Likelihood Ratio Test

Covariance matrix

Random variables

Null hypothesis

Interior

Random variable

testing

Ring

Geometry

Alternatives

Operator

Convex cone

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)

Cite this

Sasabuchi, S. (1980). A test of a multivariate normal mean with composite hypotheses determined by linear inequalities. Biometrika, 67(2), 429-439. https://doi.org/10.1093/biomet/67.2.429

A test of a multivariate normal mean with composite hypotheses determined by linear inequalities. / Sasabuchi, Shoichi.

In: Biometrika, Vol. 67, No. 2, 01.12.1980, p. 429-439.

Research output: Contribution to journal › Article

Sasabuchi, S 1980, 'A test of a multivariate normal mean with composite hypotheses determined by linear inequalities', Biometrika, vol. 67, no. 2, pp. 429-439. https://doi.org/10.1093/biomet/67.2.429

Sasabuchi S. A test of a multivariate normal mean with composite hypotheses determined by linear inequalities. Biometrika. 1980 Dec 1;67(2):429-439. https://doi.org/10.1093/biomet/67.2.429

Sasabuchi, Shoichi. / A test of a multivariate normal mean with composite hypotheses determined by linear inequalities. In: Biometrika. 1980 ; Vol. 67, No. 2. pp. 429-439.

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10.1093/biomet/67.2.429