A comparative analysis of Spearman's rho and Kendall's tau in normal and contaminated normal models

Authors:
Weichao Xu;Yunhe Hou;Y. S. Hung;Yuexian Zou
Affiliations:
Department of Automatic Control, School of Automation, Guangdong University of Technology, Guangzhou, Guangdong 510006, PR China;Department of Electrical & Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;Department of Electrical & Electronic Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;Advanced Digital Signal Processing Lab, Peking University Shenzhen Graduate School, Shenzhen, Guangdong 518055, PR China
Venue:
Signal Processing
Year:
2013

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Abstract

This paper analyzes the performances of Spearman's rho (SR) and Kendall's tau (KT) with respect to samples drawn from bivariate normal and contaminated normal populations. Theoretical and simulation results suggest that, contrary to the opinion of equivalence between SR and KT in some literature, the behaviors of SR and KT are strikingly different in the aspects of bias effect, variance, mean square error (MSE), and asymptotic relative efficiency (ARE). The new findings revealed in this work provide not only deeper insights into the two most widely used rank-based correlation coefficients, but also a guidance for choosing which one to use under the circumstances where Pearson's product moment correlation coefficient (PPMCC) fails to apply.