Dependence function for bivariate cdf's

TL;DR

This paper introduces a new function-valued measure of dependence for bivariate random variables, enabling detailed analysis and visualization of dependence structures both theoretically and empirically.

Contribution

It proposes a novel, function-valued dependence measure that enhances understanding and inference of dependence structures without relying on specific models.

Findings

The measure captures explicit dependence structures.

Theoretical properties of the measure are established.

Applications demonstrate practical utility with real and artificial data.

Abstract

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.