Testing the hypothesis of a nonrmal mean lying outside a convex cone

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Abstract
In a variety of situations a hypothesis of special nature is to be established. These situations include acceptance sampling,. bioequivalence testing, combination drug testing and others. In such situations it is proper to place the hypothesis to be established as the alternative hypothesis and the opposite statement as the null hypothesis. Ot these situations we focus on those in which the alternative hypothesis specifies a polyhedral cone for a normal mean vector. A commonly used test is the likelihood ratio (LR) test. The test statistic is a minimum of several t-statistics and yet the critical value is still a t-percentile. In addition, although the test size is exactly α , it is only attained as a limit. We generalize these results to the case of convex cone. The test statistic is expressed as a distance measure. The size property is established by an argument more complex than those previously given for polyhedral cones. A convex but nonpolyhedral cone can be encountered in comparing two polynomial regressions of degree 2 or higher. For the case of bioequivalence testing, the LR test issuperior to most existing procedures. We also consider the case when the alternative region is a double cone and obtain new and improved results.