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Robustness versus Efficiency for Nonparametric Correlation Measures

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  • Christophe Croux
  • Catherine Dehon

Abstract

Nonparametric correlation measures at the Kendall and Spearman correlation are widely used in the behavioral sciences. These measures are often said to be robust, in the sense of being resistant to outlying observations. In this note we formally study their robustness by means of their infuence functions. Since robustness of an estimator often comes at the price of a loss in precision, we compute effciencies at the normal model. A comparison with robust correlation measures derived from robust covariance matrices is made. We conclude that both Spearman and Kendall correlation measures combine good robustness properties with high effciency.

Suggested Citation

  • Christophe Croux & Catherine Dehon, 2008. "Robustness versus Efficiency for Nonparametric Correlation Measures," Working Papers ECARES 2008_002, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2008_002
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    References listed on IDEAS

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    1. Genton, Marc G. & Ma, Yanyuan, 1999. "Robustness properties of dispersion estimators," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 343-350, October.
    2. Borkowf, Craig B., 2002. "Computing the nonnull asymptotic variance and the asymptotic relative efficiency of Spearman's rank correlation," Computational Statistics & Data Analysis, Elsevier, vol. 39(3), pages 271-286, May.
    3. Falk, Michael, 1998. "A Note on the Comedian for Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 306-317, November.
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    More about this item

    Keywords

    Asymptotic Variance; Correlation; Gross-Error Sensitivity; Infuence function; Kendall correlation; Robustness; Spearman correlation.;
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