Christophe Croux (Université Catholique de Louvain), “Robustness properties of some nonparametric correlation measures”, Statistics Seminar, Toulouse: TSE, May 18, 2010, 14:00–15:30, room MD 004.
Nonparametric correlation measures as 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 influence functions and maxbias curves. Since robustness of an estimator often comes at the price of a loss in precision, we also compute statistical efficiencies 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 a bounded influence function with a high efficiency. However, when multiple outliers are present in the data, correlations based on robust covariance matrices are preferable.