Different Coefficients for Studying Dependence

Oona Rainio ()
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Oona Rainio: University of Turku

Sankhya B: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 20, 895-914

Abstract: 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. According to our results, the maximal correlation is often the best choice of these measures of dependence because it can recognize both functional and non-functional types of dependence, fulfills a certain definition of equitability relatively well, and has very high statistical power when the noise grows if there are enough observations. While Pearson’s correlation does not find symmetric non-monotonic dependence, it has the highest statistical power for recognizing linear and non-linear but monotonic dependence. The MIC is very sensitive to the noise and therefore has the weakest statistical power.

Keywords: Correlation; distance correlation; information coefficient of correlation; maximal correlation; maximal information coefficient; mutual information.; Primary 62H20; Secondary 62B10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13571-022-00295-0

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