Smoothed ranks for two or multi-sample location problems

ABSTRACT

Smoothed ranks are proposed for two or multi-sample location problems. The regular ranks in Wilcoxon's two sample test are replaced with smoothed ranks, and the shift parameter is estimated. Asymptotic properties of the smoothed rank estimator are shown and a hypothesis test is proposed. Moreover, the smoothed ranks are applied in the Kruskal–Wallis's r-sample test and the power of the test is computed using regular and smoothed ranks. Examples and Monte Carlo simulations show that the smoothed ranks perform similarly to the traditional rank based estimators under contaminated normal or non-normal populations.

KEYWORDS:

• Hodges–Lehmann
• Kruskal–Wallis
• Shift parameter
• Smoothed ranks
• Smoothing
• Two-sample location problem
• Wilcoxon

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 62G10
• 62G35

Acknowledgments

I would like to send my special thanks to the editor and the referees for their valuable comments and suggestions that contributed to improve this article.