A copula-based measure for quantifying asymmetry in dependence and associations

Abstract

Asymmetry is an inherent property of bivariate associations and therefore must not be ignored. The currently applicable dependence measures mask the potential asymmetry of the underlying dependence structure by implicitly assuming that quantity Y is equally dependent on quantity X, and vice versa, which is generally not true. We introduce the copula-based dependence measure qad that quantifies asymmetry. Specifically, qad is applicable in general situations, is sensitive to noise in data, detects asymmetry in dependence and reliably quantifies the information gain/predictability of quantity Y given knowledge of quantity X, and vice versa. Using real-world data sets, we demonstrate the relevance of asymmetry in associations. Asymmetry in dependence is a novel category of information that provides substantial information gain in analyses of bivariate associations.