Open Access
December 1995 Constructing tests for normal order-restricted inference
Arthur Cohen, Harold B. Sackrowitz, Ester Samuel-Cahn
Bernoulli 1(4): 321-333 (December 1995). DOI: 10.3150/bj/1193758709


For normal models we consider the problem of testing a null hypothesis against an order-restricted alternative. The alternative always consists of a cone minus the null space. We offer sufficient conditions for a class of tests to be complete and for unbiasedness of tests. Both sets of sufficient conditions are expressed in terms of the notion of cone order monotonicity. A method of constructing tests that are unbiased and in the complete class is given. The method yields new tests of value to many problems. Detailed applications and a simulation study are offered for testing homogeneity of means against the simple order alternative and for testing homogeneity against the matrix order alternative.


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Arthur Cohen. Harold B. Sackrowitz. Ester Samuel-Cahn. "Constructing tests for normal order-restricted inference." Bernoulli 1 (4) 321 - 333, December 1995.


Published: December 1995
First available in Project Euclid: 30 October 2007

zbMATH: 0837.62050
MathSciNet: MR1369164
Digital Object Identifier: 10.3150/bj/1193758709

Keywords: Bayes-type tests , complete class , Cone order monotonicity , cone ordering , convexity , dual cone , likelihood ratio test , matrix order alternative , Unbiased tests

Rights: Copyright © 1995 Bernoulli Society for Mathematical Statistics and Probability

Vol.1 • No. 4 • December 1995
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