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Local Dependence Test Between Random Vectors Based on the Robust Conditional Spearman’s ρ and Kendall’s τ

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Abstract

This paper introduces two local conditional dependence matrices based on Spearman’s ρ and Kendall’s τ given the condition that the underlying random variables belong to the intervals determined by their quantiles. The robustness is studied by means of the influence functions of conditional Spearman’s ρ and Kendall’s τ. Using the two matrices, we construct the corresponding test statistics of local conditional dependence and derive their limit behavior including consistency, null and alternative asymptotic distributions. Simulation studies illustrate a superior power performance of the proposed Kendall-based test. Real data analysis with proposed methods provides a precise description and explanation of some financial phenomena in terms of mathematical statistics.

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Acknowledgments

The authors thank the editor, the associate editor and the referees for their constructive comments and suggestions that have substantially improved the original manuscript.

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Authors and Affiliations

  1. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Ling-yue Zhang & Heng-jian Cui

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  1. Ling-yue Zhang
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  2. Heng-jian Cui
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Correspondence to Heng-jian Cui.

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Conflict of Interest

Heng-jian CUI is an editor-in-chief for Acta Mathematicae Applicatate Sinica (English Series) and was not involved in the editorial review or the decision to publish this article. All authors declare that there are no competing interests.

This work is supported by the State Key Program of the National Natural Science Foundation of China (No: 12031016), the National Natural Science Foundation of China (Nos: 11971324, 11901406, 12201435), the Beijing Postdoctoral Research Foundation (No: 2022-ZZ-084), the Interdisciplinary Construction of Bioinformatics and Statistics, and the Academy for Multidisciplinary Studies, Capital Normal University.

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Zhang, Ly., Cui, Hj. Local Dependence Test Between Random Vectors Based on the Robust Conditional Spearman’s ρ and Kendall’s τ. Acta Math. Appl. Sin. Engl. Ser. 39, 491–510 (2023). https://doi.org/10.1007/s10255-023-1073-4

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  • DOI: https://doi.org/10.1007/s10255-023-1073-4

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