Seminars 2008 — Abstracts
Friday, October 24
Speaker:
John Robinson,
Sydney
Title:
Robust permutation tests for two samples
Abstract: We consider robust permutation tests for a location shift in the two sample case based on estimating equations, comparing the test statistics based on a score function and an M-estimate. First we obtain a form for other tests so that the exact tests may be carried out using the same algorithms as used for permutation tests based on the mean. Then, by developing a large deviation result for sampling from a finite population, we obtain the Bahadur slopes 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 on Bahadur slopes.
