A Dependence Function for Visualizing Association Structure in Bivariate Distributions

Measuring the strength of dependence of random variables is an important problem in statistical practice. In this paper, we review a function valued measure of dependence of two random variables, where introduced by Ledwina [1]. This function allows one to study and visualize explicit dependence structure, both in some theoretical models and empirically, with-out prior model structure. It provides a comprehensive view of association structure and makes possible much detailed inference than based on standard numeric measures of association. We present theoretical properties of the measure of dependence and discuss in detail estimation and application of a copula-based variant of it. An artificial data example illustrate the behavior and practical utility of the measure and its estimator.

Keywords:

Copula function , Dependence measures , Graph-ical method , Local correlation.