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 ζ 1 overcoming the just mentioned problem was introduced in 2011. ζ 1 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 ζ 1 n for ζ 1 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 ζ 1 n 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.

中文翻译：

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估计二元分布的尺度不变的有向依赖性

摘要 依赖的不对称性是二元概率分布的固有特性。由于是对称的，常用的相关性度量，例如 Pearson 的 r 或 Spearman 的 ρ 掩码不对称性，并隐含地假设随机变量 Y 同样依赖于随机变量 X，反之亦然。2011 年引入了一个基于 copula，因此称为 ζ 1 的尺度不变依赖度量，克服了刚才提到的问题。 ζ 1 获得 [ 0 , 1 ] 中的值，当且仅当 X 和 Y 独立时它为 0，并且1 当且仅当 Y 是 X 的可测函数。使用所谓的经验棋盘式 copula 可以为 ζ 1 构建一个估计量 ζ 1 n ，它在完全一般性上是高度一致的，即对底层 copula 没有任何平滑假设。