Equitability of Dependence Measure
This work addresses a fundamental issue in statistical dependence measurement for applications like variable selection and brain network analysis, but it is incremental as it refines existing definitions rather than proposing a new method.
The paper tackles the problem of equitability in dependence measures, showing that it is theoretically impossible for a continuous score to give similar values to equally noisy relationships of different types. It introduces a new definition called power-equitable (weak-equitable) and demonstrates through simulation that HHG and Copula Dependence Coefficient (CDC) satisfy this property.
Measuring dependence between two random variables is very important, and critical in many applied areas such as variable selection, brain network analysis. However, we do not know what kind of functional relationship is between two covariates, which requires the dependence measure to be equitable. That is, it gives similar scores to equally noisy relationship of different types. In fact, the dependence score is a continuous random variable taking values in $[0,1]$, thus it is theoretically impossible to give similar scores. In this paper, we introduce a new definition of equitability of a dependence measure, i.e, power-equitable (weak-equitable) and show by simulation that HHG and Copula Dependence Coefficient (CDC) are weak-equitable.