Nonparametric simultaneous tests for location and scale testing: a comparison of several methods

The two-sample location-scale problem arises in many situations like climate dynamics, bioinformatics, medicine and finance. To address this problem, the nonparametric approach is considered because in practice, the normal assumption is often not fulfilled or the observations are too few to rely on the central limit theorem, and moreover outliers, heavy tails and skewness may be possible. In these situations, a nonparametric test is generally more robust and powerful than a parametric test. Various nonparametric tests have been proposed for the two-sample location-scale problem. In particular we consider tests due to Lepage, Cucconi, Podgor-Gastwirth, Neuhäuser, Zhang and Murakami. So far all these tests have not been compared. Moreover, for the Neuhäuser test and the Murakami test, the power has not been studied in detail. It is the aim of the paper to review and compare these tests for the jointly detection of location and scale changes by means of a very detailed simulation study. It is shown that both the Podgor-Gastwirth test and the computationally simpler Cucconi test are preferable. Two actual examples within the medical context are discussed.