Smoothed alternatives of the two-sample median and Wilcoxon's rank sum tests. Issue 5 (3rd September 2018)

• Record Type: Journal Article
• Authors: Moriyama, Taku; Maesono, Yoshihiko
• Is Part Of: Statistics. Volume 52:Issue 5(2018)
• Page Start: 1096
• Page End: 1115
• Publication Date: 2018-09-03
• Subjects: Median test -- Wilcoxon's rank sum test -- kernel estimator -- significance probability; 62G10 -- 62G20; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2018.1469634
• Languages: English
• ISSNs: 0233-1888

Abstract

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.