BAHADUR SLOPES FOR COMPARISONS OF TESTS BASED ON RESAMPLING

Summary LetX1,…,Xnbe random variables symmetric about θ from a common unknown distribution Fθ(x) =F(x–θ). To test the null hypothesisH0:θ= 0 against the alternativeH1:θ > 0, permutation tests can be used at the cost of computational difficulties. This paper investigates alternative tests that are computationally simpler, notably some bootstrap tests which are compared with permutation tests. Of these the symmetrical bootstrap‐f test competes very favourably with the permutation test in terms of Bahadur asymptotic efficiency, so it is a very attractive alternative.