SOME GENERAL RESULTS ON LEAST FAVORABLE PARAMETER CONFIGURATIONS WITH SPECIAL REFERENCE TO EQUIVALENCE TESTING AND THE RANGE STATISTIC

The problem of hypotheses testing where equivalence is stated as the alternative hypothesis is investigated. With respect to a class of absolutely continuous probability distributions with location parameter v element of R(k), k greater-than-or-equal-to 2, equivalence is defined in terms of the range of the components of v. For non-randomized tests having certain reasonable invariance properties, general results for the extremal points of the power function over both the hypothesis of non-equivalence and subsets of the alternative are provided. The power problem is completely solved, among other things, for tests based on the range statistic. Finally, the equicorrelated normal case is treated in detail and sample sizes for controlling both error levels in equivalence testing are given.