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.


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