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We introduce a new type of influence function, the asymptotic expectedsensitivity function, which is often equivalent to but mathematically moretractable than the traditional one based on the Gateaux derivative. Toillustrate, we study the robustness of some important rank correlations,including Spearman's and Kendall's correlations, and the recently developedChatterjee's correlation.

Asymptotic expected sensitivity function and its applications to nonparametric correlation estimators