A measure of general functional dependence between two continuous variables

Nuo Xu, Xuan Huang and Samuel Huang

Communications in Statistics - Theory and Methods, 2017, vol. 46, issue 9, 4327-4352

Abstract: Existing measures in the literature that are specifically concerned with testing and measuring independence between two continuous variables are all based on examining the definition of independence, i.e., FXY(x, y) = FX(x)FY(y). A new measure is constructed uniquely in this paper that uses the absolute value of first difference on adjacent ranks of one variable with respect to the other. This measure captures the degree of functional dependence attributable to the amount of randomness and the complexity of the underlying bivariate dependence structure in a commensurate way that existing coefficients are incapable of. As a test statistic of independence, this measure is shown to have comparable or better power than existing statistics against a wide range of alternative hypotheses that consist of functional and multivalued relational dependence with additive noise.

Date: 2017
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DOI: 10.1080/03610926.2015.1081951

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