  Measuring a strength of dependence of random variables is an important
problem in statistical practice. In this paper, we propose a new function
valued measure of dependence of two random variables. It allows one to study
and visualize explicit dependence structure, both in some theoretical models
and empirically, without prior model structure. This 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 new measure of dependence and discuss in detail estimation
and application of copula-based variant of it. Some artificial and real data
examples illustrate the behavior and practical utility of the measure and its
estimator.
