Robust permutation tests for one sample |
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| Institution: | 1. Department of Medicine, The University of Chicago, MC6026, 5841 South Maryland Ave, Chicago, IL 60637, USA;2. Department of Health Studies, University of Chicago, Chicago, IL, USA;3. Department of Nutritional Sciences, University of Wisconsin, Madison, WI, USA;1. Department of Psychiatry, Faculty of Medicine, The Chinese University of Hong Kong, Shatin, NT, Hong Kong SAR;2. Genetic Epidemiology Research Branch, Intramural Research Program, National Institute of Mental Health, Amsterdam, The Netherlands;3. GGZ in Geest/VU University Medical Center, Amsterdam, Department of Psychiatry, EMGO Institute for Health and Care Research and Neuroscience Campus Amsterdam, VU University Medical Center/GGZ in Geest, Amsterdam, The Netherlands;4. Brain & Mind Research Institute, University of Sydney Camperdown, NSW 2050, Australia |
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| Abstract: | We consider robust permutation tests based on an estimating equation comparing the test statistics based on the score function with those based on the M-estimate. First we obtain a form for the 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 compare the efficiencies of the tests in two cases, equivalent to the sign test and a test based on Huber scores, showing that they are equivalent in the Pitman sense but that they have different Bahadur slopes with neither exceeding the other over the whole range. |
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