Nonparametric Dependence Measures Based on Spacings under Extreme Value Domains

Abstract

Classical dependence measures such as Kendall’s τ , Bergsma-Dassios τ∗, and Székely-Rizzo’s distance covariance often exhibit suboptimal performance when data arise from distributions characterized by heavy tails, light tails, or bounded supports—typical of the Gumbel, Fréchet, and Weibull domains of attraction. To address these limitations, we introduce a novel framework that leverages marginal spacings to redefine these nonparametric dependence measures. Through comprehensive simulation studies, theoretical derivations, and an empirical data analysis on the Airfoil Self-Noise dataset, we explore the asymptotic power, efficiency, and robustness of the resulting spacing-based statistics under diverse dependence structures and a range of tail indices α. Our results demonstrate that spacingbased methods provide enhanced sensitivity and more reliable inference in scenarios dominated by extreme marginal behaviors, making them particularly well-suited for applications in fields such as risk management, environmental studies, and extreme value theory.