  This paper introduces a new property of estimators of the strength of
statistical association, which helps characterize how well an estimator will
perform in scenarios where dependencies between continuous and discrete random
variables need to be rank ordered. The new property, termed the estimator
response curve, is easily computable and provides a marginal distribution
agnostic way to assess an estimator's performance. It overcomes notable
drawbacks of current metrics of assessment, including statistical power, bias,
and consistency. We utilize the estimator response curve to test various
measures of the strength of association that satisfy the data processing
inequality (DPI), and show that the CIM estimator's performance compares
favorably to kNN, vME, AP, and H_{MI} estimators of mutual information. The
estimators which were identified to be suboptimal, according to the estimator
response curve, perform worse than the more optimal estimators when tested with
real-world data from four different areas of science, all with varying
dimensionalities and sizes.
