Maximum test and adaptive test for the general two-sample problem

Abstract

An extension of the omnibus test statistic of Ebner et al. [A new omnibus test of fit based on a characterization of the uniform distribution. Statistics. 2022;56:1364–1384. doi: 10.1080/02331888.2022.2133121] is considered for the general two-sample alternative. In addition, using the extension this paper introduces a maximum test statistic and an adaptive test statistic for testing the equality of two distributions. The power performance in various situations is investigated for continuous and discrete distributions. Simulation studies based on Monte-Carlo show that the proposed test statistics are good competitors of the existing nonparametric test statistics. The proposed test statistic displays outstanding performance in certain situations, and is illustrated using real data. Finally, we offer some concluding remarks.

Keywords:

• Adaptive test
• maximum test
• nonparametric test
• selector

Acknowledgements

The authors wish to thank the Editor, Associate Editor and three anonymous reviewers for their kind cooperation. We appreciate the voluntary contributions of the reviewers affording time to sincerely read the early version of the manuscript, and their comments helped improve the general presentation of the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).