A class of percentile modified Lepage-type tests
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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.
KeywordsNonparametric tests Permutation tests Rank tests Location-scale tests Mahalanobis distance
Mathematics Subject Classification62G10 62G09 62P10
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Conflict of interest
All authors declares that they have no conflict of interest.
- Cucconi O (1968) Un nuovo test non parametrico per il confronto tra due gruppi campionari. Giornale degli Economisti 27:225–248Google Scholar
- Kössler, W (2006) Asymptotic Power and Efficiency of Lepage-Type Tests for the Treatment of Combined Location-Scale Alternatives. Informatik-Bericht Nr. 200, Humboldt-Universität zu Berlin, 1-26. https://edoc.hu-berlin.de/handle/18452/3114. Accessed 22 Oct 2016
- Ludbrook J, Dudley H (1998) Why permutation tests are superior to t and F tests in biomedical research. The Am Stat 52:127–132Google Scholar