Estimating scale-invariant directed dependence of bivariate distributions

Robert R. Junker, Florian Griessenberger and Wolfgang Trutschnig

Computational Statistics & Data Analysis, 2021, vol. 153, issue C

Abstract: Asymmetry of dependence is an inherent property of bivariate probability distributions. Being symmetric, commonly used dependence measures such as Pearson’s r or Spearman’s ρ mask asymmetry and implicitly assume that a random variable Y is equally dependent on a random variable X as vice versa. A copula-based, hence scale-invariant dependence measure called ζ1 overcoming the just mentioned problem was introduced in 2011. ζ1 attains values in [0,1], it is 0 if, and only if X and Y are independent, and 1 if, and only if Y is a measurable function of X. Working with so-called empirical checkerboard copulas allows to construct an estimator ζ1n for ζ1 which is strongly consistent in full generality, i.e., without any smoothness assumptions on the underlying copula. The R-package qad (short for quantification of asymmetric dependence) containing the estimator ζ1n is used both, to perform a simulation study illustrating the small sample performance of the estimator as well as to estimate the directed dependence between some global climate variables as well as between world development indicators.

Keywords: Asymmetry; Copula; Correlation; Dependence; Direction; Invariance (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:153:y:2021:i:c:s0167947320301493

DOI: 10.1016/j.csda.2020.107058

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