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Multivariate Extension Application for Spearman’s Footrule Correlation Coefficient

Author

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  • 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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