A Copula‐Based Non‐parametric Measure of Regression Dependence

Holger Dette · Karl Friedrich Siburg · Pavel A. Stoimenov

94 citations0/0 files storedScandinavian Journal of Statistics

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Financial Risk and Volatility Modeling Statistical Methods and Inference Advanced Statistical Methods and Models

Abstract

Abstract. This article presents a framework for comparing bivariate distributions according to their degree of regression dependence. We introduce the general concept of a regression dependence order (RDO). In addition, we define a new non‐parametric measure of regression dependence and study its properties. Besides being monotone in the new RDOs, the measure takes on its extreme values precisely at independence and almost sure functional dependence, respectively. A consistent non‐parametric estimator of the new measure is constructed and its asymptotic properties are investigated. Finally, the finite sample properties of the estimate are studied by means of a small simulation study.

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References

1999An Introduction to Copulas 1981On Nonparametric Measures of Dependence for Random Variables 2004Weak convergence of empirical copula processes 2004Goodness-of-fit tests for copulas 1992Copulas and Markov processes 1984On measures of concordance 2003Nonparametric estimation of copulas for time series 2007Nonparametric estimation of copula functions for dependence modelling

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