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Asymptotic expected sensitivity function and its applications to measures of monotone association

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  • Qingyang Zhang

    (University of Arkansas)

Abstract

We introduce a new type of influence function, the asymptotic expected sensitivity function, which is often equivalent to but mathematically more tractable than the traditional one based on the Gâteaux derivative. To illustrate, we study the robustness of some important measures of association, including Spearman’s rank correlation and Kendall’s concordance measure, and the recently developed Chatterjee’s correlation.

Suggested Citation

  • Qingyang Zhang, 2024. "Asymptotic expected sensitivity function and its applications to measures of monotone association," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 877-896, October.
    • Handle: RePEc:spr:aistmt:v:76:y:2024:i:5:d:10.1007_s10463-024-00910-z
    DOI: 10.1007/s10463-024-00910-z
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    References listed on IDEAS

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    1. Zhang, Qingyang, 2023. "On the asymptotic null distribution of the symmetrized Chatterjee’s correlation coefficient," Statistics & Probability Letters, Elsevier, vol. 194(C).
    2. Croux, Christophe, 1998. "Limit behavior of the empirical influence function of the median," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 331-340, March.
    3. Holger Dette & Karl F. Siburg & Pavel A. Stoimenov, 2013. "A Copula-Based Non-parametric Measure of Regression Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(1), pages 21-41, March.
    4. Christophe Croux & Catherine Dehon, 2010. "Influence functions of the Spearman and Kendall correlation measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 497-515, November.
    5. Sourav Chatterjee, 2021. "A New Coefficient of Correlation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 2009-2022, October.
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