Maximum Test versus Adaptive Tests for the Two-Sample Location Problem

Markus Neuhauser, Herbert Buning and Ludwig Hothorn

Journal of Applied Statistics, 2004, vol. 31, issue 2, 215-227

Abstract: For the non-parametric two-sample location problem, adaptive tests based on a selector statistic are compared with a maximum and a sum test, respectively. When the class of all continuous distributions is not restricted, the sum test is not a robust test, i.e. it does not have a relatively high power across the different possible distributions. However, according to our simulation results, the adaptive tests as well as the maximum test are robust. For a small sample size, the maximum test is preferable, whereas for a large sample size the comparison between the adaptive tests and the maximum test does not show a clear winner. Consequently, one may argue in favour of the maximum test since it is a useful test for all sample sizes. Furthermore, it does not need a selector and the specification of which test is to be performed for which values of the selector. When the family of possible distributions is restricted, the maximin efficiency robust test may be a further robust alternative. However, for the family of t distributions this test is not as powerful as the corresponding maximum test.

Keywords: Location-shift model; measures of skewness and tailweight; maximin efficiency robust test; non-parametric tests; two-sample location problem; selector statistic (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1080/0266476032000148876

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