New weighted rank correlation coefficients sensitive to agreement on top and bottom rankings

ABSTRACT

Three new weighted rank correlation coefficients are proposed which are sensitive to both agreement on top and bottom rankings. The first one is based on the weighted rank correlation coefficient proposed by Maturi and Abdelfattah [13], the second and the third are based on the order statistics and the quantiles of the Laplace distribution, respectively. The limiting distributions of the new correlation coefficients under the null hypothesis of no association between the rankings are presented, and a summary of the exact and approximate quantiles for these coefficients is provided. A simulation study is performed to compare the performance of Kendall's tau, Spearman's rho, and the new weighted rank correlation coefficients in detecting the agreement on the top and the bottom rankings simultaneously. Finally, examples are given for illustration purposes, including a real data set from financial market indices.

KEYWORDS:

• Weighted correlation
• measures of agreement
• measures of association
• rank correlation
• Laplace distribution
• order statistics

Acknowledgments

The author would like to thank the anonymous reviewers for their valuable comments that help to improve the paper. Also I would like to thank Simos Meintanis and George Iliopoulos for providing the data used in Example 5.2.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. http://www.commanster.eu/rcode.html.

2. The R codes are available on request from the author.