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Influence functions of the Spearman and Kendall correlation measures

Abstract

Nonparametric correlation estimators as the Kendall and Spearman correlation are widely used in the applied sciences. They are often said to be robust, in the sense of being resistant to outlying observations. In this paper we formally study their robustness by means of their influence functions and gross-error sensitivities. Since robustness of an estimator often comes at the price of an increased variance, we also compute statistical efficiencies at the normal model. We conclude that both the Spearman and Kendall correlation estimators combine a bounded and smooth influence function with a high efficiency. In a simulation experiment we compare these nonparametric estimators with correlations based on a robust covariance matrix estimator.

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Acknowledgments

We would like to thank the two reviewers for their careful reading of our manuscript and their useful comments.

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This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Correspondence to Christophe Croux.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Croux, C., Dehon, C. Influence functions of the Spearman and Kendall correlation measures. Stat Methods Appl 19, 497–515 (2010). https://doi.org/10.1007/s10260-010-0142-z

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  • DOI: https://doi.org/10.1007/s10260-010-0142-z

Keywords

  • Asymptotic variance
  • Correlation
  • Gross-error sensitivity
  • Influence function
  • Kendall correlation
  • Robustness
  • Spearman correlation

Mathematics Subject Classification (2000)

  • 65G35
  • 62F99