On Asymmetric Properties of the Correlation Coeffcient in the Regression Setting

By Y. Dodge, V. Rousson. 2001

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Pairwise Likelihood Ratios for Estimation of Non-Gaussian Structural Equation Models (2013, methodology): “Our measure is related to the directionality measure proposed by Dodge and Rousson (2001), which in our notation would be: ˜ R DR (x, y) = [ ˆ E{x 2 y}] 2 − [E{xy 2 }] 2 (14) which has the advantage of of being particularly simple, and does not require the skewnesses to be of any particular sign.”
A Linear Non-Gaussian Acyclic Model for Causal Discovery (2006, background): “However, assuming non-gaussianity, one can actually discover the direction of causality, as shown by Dodge and Rousson (2001); Shimizu and Kano (2006).”
Independent component analysis: recent advances (2013, unknown): “(An earlier approach used cumulants (Dodge and Rousson, 2001).)”
Extensions of ICA for Causality Discovery in the Hong Kong Stock Market (2006, background): “Recently, it has been shown that the non-Gaussianity distribution of the variables allows us to distinguish the explanatory variable from the response variable, and consequently, to identify the full causal model [ 2 ,11].”
Asymmetric properties of the Pearson correlation coefficient: Correlation as the negative association between linear regression residuals (2016, methodology): “Table 1 shows the parameter recovery of Equation (5) and the asymmetric formulas of the Pearson correlation coefficient based on manifest variables X and Y given in Dodge and Rousson (2001) for samples sizes of 50, 250, and 500.”