Local Dependence Test Between Random Vectors Based on the Robust Conditional Spearman’s ρ and Kendall’s τ
Acta Mathematicae Applicatae Sinica(2023)
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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Key words
local dependence,influence function l]rank correlation,U-statistic
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