An Adaptive Test for the Two-Sample Location Problem Based on U-Statistics

Abstract

For the two-sample location problem with continuous data we consider a general class of tests, all members of it are based on U-statistics. The asymptotic efficacies are investigated in detail. We construct an adaptive test where all statistics involved are suitably chosen U-statistics. It is shown that the proposed adaptive test has good asymptotic and finite sample power properties.

Keywords:

• Asymptotic efficacy
• Asymptotic power
• Simulation study
• Skewness
• Tailweight
• Wilcoxon–Mann–Whitney test

Mathematics Subject Classification:

• 62G10
• 62G20

Acknowledgments

The authors are grateful to the editor and the referees who gave valuable hints on an improvement of an earlier version of this article.