Robust permutation tests for two samples

We consider robust permutation tests for a location shift in the two sample case based oil estimating equations, comparing the test statistics based oil a score function and an M-estimate. First we obtain a form for both tests so that the exact tests may be carried out using the same algorithms as used for permutation tests based on the mean. Then we obtain the Bahadur of the tests in these two statistics, giving numerical results for two cases equivalent to a test based on Huber scores and a particular case of this related to a median test. We show that they have different Bahadur slopes with neither exceeding the other over the whole range. Finally, we give some numerical results illustrating the robustness properties of the tests and confirming the theoretical results oil Bahadur slopes. (C) 2008 Elsevier B.V. All rights reserved.