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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
DOI: https://doi.org/10.1090/S0002-9939-01-05824-5
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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  • 1. Berger, R. L. (1989), Uniformly more powerful tests for hypotheses concerning linear inequalities and normal means, J. Amer. Statist. Assoc., 84, 192-199. MR 90k:62117
  • 2. Berger, R. L. and Hsu, J. C. (1996), Bioequivalence trials, intersection-union tests, and equivalence confidence sets, Statist. Sci., 11, 283-302. MR 98e:62046
  • 3. Laska, E. M. and Meisner, M. J. (1989), Testing whether an identified treatment is best, Biometrics, 45, 1139-1151. MR 91d:62059
  • 4. Liu, H. and Berger, R. L. (1995), Uniformly more powerful, one-sided tests for hypotheses about linear inequalities, Ann. Statist., 23, 55-72. MR 96m:62108
  • 5. Lukacs, E. (1955), A characterization of the gamma distribution, Ann. Math. Statist., 26, 319-324. MR 16:1034b
  • 6. McDermott, M. P. and Wang, Y. (2001), Construction of uniformly more powerful tests for hypotheses about linear inequalities, J. Statist. Plan. Inf. (to appear).
  • 7. Sasabuchi, S. (1980), A test of a multivariate normal mean with composite hypotheses determined by linear inequalities, Biometrika, 67, 429-439. MR 82a:62078
  • 8. Sasabuchi, S. (1988), A multivariate test with composite hypotheses determined by linear inequalities when the covariance matrix has an unknown scale factor, Mem. Fac. Sci., Kyushu Univ. Ser. A, 42, 9-19. MR 89k:62075

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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: https://doi.org/10.1090/S0002-9939-01-05824-5
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

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