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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniformly more powerful tests for hypotheses about linear inequalities when the variance is unknown


Authors: Yining Wang and Michael P. McDermott
Journal: Proc. Amer. Math. Soc. 129 (2001), 3091-3100
MSC (2000): Primary 62F03; Secondary 62F04, 62H15
Published electronically: May 10, 2001
MathSciNet review: 1840116
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Abstract: Let X be a $p$-dimensional normal random vector with unknown mean $\mu $ and covariance matrix $\Sigma =\sigma ^{2}\Sigma _{0}$, where $\Sigma _{0}$ is a known matrix and $\sigma ^{2}$ an unknown parameter. This paper gives a test for the null hypothesis that $\mu $ lies either on the boundary or in the exterior of a closed, convex polyhedral cone versus the alternative hypothesis that $\mu $ lies in the interior of the cone. Our test is uniformly more powerful than the likelihood ratio test.


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Additional Information

Yining Wang
Affiliation: Schering-Plough Research Institute, 2015 Galloping Hill Road, K-15-2, 2315, Kenilworth, New Jersey 07033-0539
Email: wayne.wang@spcorp.com

Michael P. McDermott
Affiliation: Department of Biostatistics, University of Rochester, 601 Elmwood Avenue, Box 630, Rochester, New York 14642
Email: mikem@bst.rochester.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05824-5
PII: S 0002-9939(01)05824-5
Keywords: Conditional distribution, likelihood ratio test, one-sided testing, polyhedral cone
Received by editor(s): May 13, 1998
Received by editor(s) in revised form: December 14, 1999
Published electronically: May 10, 2001
Communicated by: Wei Y. Loh
Article copyright: © Copyright 2001 American Mathematical Society