The partial copula: Properties and associated dependence measures

TL;DR

This paper explores the partial copula, a generalization of partial correlation, analyzing its properties and related dependence measures to better understand conditional dependence between variables.

Contribution

It provides a comprehensive explanation of the partial copula and investigates the properties of associated partial dependence measures, advancing the theoretical understanding.

Findings

Partial copula generalizes partial correlation.

Properties of partial copula are thoroughly analyzed.

Associated dependence measures are examined.

Abstract

The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial correlation coefficient, and investigate several of its properties. In addition, properties of some associated partial dependence measures are examined.