A class of percentile modified Lepage-type tests

The two-sample problem usually tests for a difference in location. However, there are many situations, for example in biomedicine, where jointly testing for difference in location and variability may be more appropriate. Moreover, heavy-tailed data, outliers and small-sample sizes are common in biomedicine and in other fields. These considerations make the use of nonparametric methods more appealing than parametric ones. The aim of the paper is to contribute to the literature about nonparametric simultaneous location and scale testing. More precisely, several existing tests are generalized and unified, and a new class of tests based on the Mahalanobis distance between the percentile modified test statistics for location and scale differences is introduced. The asymptotic distributions of the test statistics are obtained, and small-sample size behaviour of the tests is studied and compared to other tests via Monte Carlo simulations. It is shown that the proposed class of tests performs well when there are differences in both location and variability. A practical application is presented.