The Inadmissibility of Linear Rank Tests Under Bahadur Efficiency

Abstract

Hajek (1974) has shown that in the two-sample problem the best exact slope for a test of randomness against any particular member of a large class of alternative hypotheses is attained by a linear rank test. Here a new class of two-sample rank tests is constructed, and it is shown that for each linear test there exists a test within the new class which is always at least as efficient in terms of exact Bahadur efficiency irrespective of which alternative hypothesis, is tested. Conditions are provided under which the new test is strictly more efficient than the linear rank test. Some comments are made about the practical applicability of the new class of tests.