Smoothed alternatives of the two-sample median and Wilcoxon's rank sum tests

ABSTRACT

We discuss smoothed rank statistics for testing the location shift parameter of the two-sample problem. They are based on discrete test statistics – the median and Wilcoxon's rank sum tests. For the one-sample problem, Maesono et al. [Smoothed nonparametric tests and their properties. arXiv preprint. 2016; ArXiv:1610.02145] reported that some nonparametric discrete tests have a problem with their p-values because of their discreteness. The p-values of Wilcoxon's test are frequently smaller than those of the median test in the tail area. This leads to an arbitrary choice of the median and Wilcoxon's rank sum tests. To overcome this problem, we propose smoothed versions of those tests. The smoothed tests inherit the good properties of the original tests and are asymptotically equivalent to them. We study the significance probabilities and local asymptotic powers of the proposed tests.

KEYWORDS:

• Median test
• Wilcoxon's rank sum test
• kernel estimator
• significance probability

MSC 2010 SUBJECT CLASSIFICATIONS:

• 62G10
• 62G20

Acknowledgments

The authors appreciate the editor's and referees' valuable comments that helped us to improve this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors gratefully acknowledge the Japan Society for the Promotion of Science, JSPS KAKENHI Grant Nos. JP15K11995 (Exploratory Research) and JP16H02790 (Scientific Research(B)).