A test statistic with a ranking method based on the Jeffreys divergence measure

Abstract

Nonparametric two-sample tests are important statistical procedures in many scientific fields. The test statistic has been derived from the Kullback–Liebler divergence between two empirical distribution functions. This study modifies a nonparametric two-sample test statistic using a ranking method. The modified test statistic is shown to be based on the Jeffreys divergence measure. The exact critical value of the proposed test statistic is derived for small sample sizes. Simulations are used to investigate the power of the proposed test statistic for the location alternative and for any difference between distributions, with various population distributions, for small sample sizes.

KEYWORDS:

• Jeffreys divergence measure
• Kullback-Liebler divergence measure
• power comparison
• ranking method

Acknowledgments

The authors would like to thank the editor and the referee for their valuable comments and suggestions to improve this paper. The research of the first author was supported by JSPS KAKENHI Grant Number JP18K11199.