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Multivariate Extension Application for Spearman’s Footrule Correlation Coefficient

Author

Listed:
  • Liqi Xia

    (School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China)

  • Sami Ullah

    (School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China)

  • Li Guan

    (School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China)

Abstract

This paper presents a simplified and computationally feasible multivariate extension. A correlation matrix is constructed using pairwise Spearman’s footrule correlation coefficients, and these coefficients are shown to jointly converge to a multivariate normal distribution. A global test statistic based on the Frobenius norm of this matrix asymptotically follows a weighted sum of chi-square distributions. Simulation studies and two real-world applications (a sensory analysis of French Jura wines and the characterization of plant leaf specimens) demonstrate the practical utility of the proposed method, bridging the gap between theoretical rigor and practical implementation in multivariate nonparametric inference.

Suggested Citation

  • Liqi Xia & Sami Ullah & Li Guan, 2025. "Multivariate Extension Application for Spearman’s Footrule Correlation Coefficient," Mathematics, MDPI, vol. 13(9), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1527-:d:1650095
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    References listed on IDEAS

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    3. Manuel Úbeda-Flores, 2005. "Multivariate versions of Blomqvist’s beta and Spearman’s footrule," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 781-788, December.
    4. Javad Behboodian & Ali Dolati & Manuel Úbeda-Flores, 2007. "A multivariate version of Gini's rank association coefficient," Statistical Papers, Springer, vol. 48(2), pages 295-304, April.
    5. Hongjian Shi & Mathias Drton & Fang Han, 2022. "Distribution-Free Consistent Independence Tests via Center-Outward Ranks and Signs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 395-410, January.
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    7. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
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