A measure of general functional dependence between two continuous variables. Issue 9 (3rd May 2017)

• Record Type: Journal Article
• Authors: Xu, Nuo; Huang, Xuan; Huang, Samuel
• Is Part Of: Communications in statistics. Volume 46:Issue 9(2017)
• Page Start: 4327
• Page End: 4352
• Publication Date: 2017-05-03
• Subjects: Correlation coefficient -- degree of functional dependence -- statistical power analysis -- test of independence; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2015.1081951
• Languages: English
• ISSNs: 0361-0926

Abstract

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.