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Title: A measure of multivariate conditional dependence and its estimation Authors:  Wolfgang Trutschnig - University of Salzburg (Austria) [presenting]
Florian Griessenberger - University of Salzburg (Austria)
Abstract: Working with so-called linkages allows constructing a multivariate, copula-based dependence measure zeta quantifying the strength of dependence of a real-valued (continuous) random variable $Y$ on a $d$-dimensional (continuous) random vector $X$. Zeta attains values in [0,1], is 0 if and only if $X$ and $Y$ are independent and 1 if and only if $Y$ is a function of $X$ (in which case we speak of complete dependence of $Y$ on $X$). Various additional properties of zeta are discussed, as well as related concepts like the underlying equivalent metrics which induce the dependence measure. Moreover, a strongly consistent estimator for zeta which does not require any regularity assumptions on the underlying copula and hence works in full generality is constructed, its speed of convergence is discussed and illustrated in terms of some examples ranging from independence to complete dependence.