Copula Index for Detecting Dependence and Monotonicity between Stochastic Signals

Abstract

This paper introduces a nonparametric copula-based index for detecting the strength and monotonicity structure of linear and nonlinear statistical dependence between pairs of random variables or stochastic signals. Our index, termed Copula Index for Detecting Dependence and Monotonicity (CIM), satisfies several desirable properties of measures of association, including Renyi's properties, the data processing inequality (DPI), and consequently self-equitability. Synthetic data simulations reveal that the statistical power of CIM compares favorably to other state-of-the-art measures of association that are proven to satisfy the DPI. Simulation results with real-world data reveal the CIM's unique ability to detect the monotonicity structure among stochastic signals to find interesting dependencies in large datasets. Additionally, simulations show that the CIM shows favorable performance to estimators of mutual information when discovering Markov network structure.