  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.
