Copula Index for Detecting Dependence and Monotonicity between Stochastic Signals
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This paper introduces a nonparametric copula-based approach for detecting the strength and uniquely, the monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals, termed CIM. CIM satisfies the data processing inequality and is, consequently, a self-equitable metric. Simulation results using synthetic datasets reveal that the CIM compares favorably to other state-of-the-art measures of association that satisfy the data processing inequality, including the estimators of mutual information based on k-nearest neighbors, k-NN, adaptive partitioning, AP, and the von-Mises expansion, vME. Additionally, CIM performs similarly to other state-of-the-art statistical dependency metrics, including the Maximal Information Coefficient (MIC), Randomized Dependency Coefficient (RDC), distance correlation (dCor), copula correlation (Ccor), and the Copula Statistic (CoS) in both statistical power and sample size requirements. Simulations using real world data highlight the importance of understanding the monotonicity structure of the dependence.
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