Different coefficients for studying dependence

TL;DR

This paper compares various statistical dependence measures through simulations, evaluating their effectiveness in capturing dependence under different conditions such as noise and sample size.

Contribution

It provides a comprehensive simulation-based comparison of multiple dependence coefficients, highlighting their relative strengths and limitations.

Findings

Distance correlation performs well in generality and power.

MIC shows high equitability across dependence types.

Pearson's correlation is limited to linear relationships.

Abstract

Through computer simulations, we research several different measures of dependence, including Pearson's and Spearman's correlation coefficients, the maximal correlation, the distance correlation, a function of the mutual information called the information coefficient of correlation, and the maximal information coefficient (MIC). We compare how well these coefficients fulfill the criteria of generality, power, and equitability. Furthermore, we consider how the exact type of dependence, the amount of noise and the number of observations affect their performance.