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Constructing tests for normal order-restricted inference. (English) Zbl 0837.62050

Summary: 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.

MSC:

62H15 Hypothesis testing in multivariate analysis
62F30 Parametric inference under constraints
62C07 Complete class results in statistical decision theory
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