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Statistical Dependence: Beyond Pearson's ρ
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DOI：10.1214/21-STS823.png)
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Abstract
En 中文
Pearson's rho is the most used measure of statistical dependence. It gives a complete characterization of dependence in the Gaussian case, and it also works well in some non-Gaussian situations. It is well known; however, that it has a number of shortcomings; in particular, for heavy tailed distributions and in nonlinear situations, where it may produce misleading, and even disastrous results. In recent years, a number of alternatives have been proposed. In this paper, we will survey these developments, especially results obtained in the last couple of decades. Among measures discussed are the copula, distribution-based measures, the distance covariance, the HSIC measure popular in machine learning and finally the local Gaussian correlation, which is a local version of Pearson's rho. Throughout, we put the emphasis on conceptual developments and a comparison of these. We point out relevant references to technical details as well as comparative empirical and simulated experiments. There is a broad selection of references under each topic treated.
Keywords:
Statistical dependence
Pearson's rho
nonlinear dependence
distance covariance
HSIC
mutual information
local Gaussian correlation
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