Nonparametric estimation of tail dependence


Dependencies of extreme events (extremal dependencies) are attracting an increasing attention in modern risk management. In practice, the concept of tail dependence represents the current standard to describe the amount of extremal dependence. In theory, multivariate extreme-value theory (EVT) turns out to be the natural choice to model the latter dependencies. The present paper embeds tail dependence into the concept of tail copulae which describes the dependence structure in the tail of multivariate distributions but works more generally. Various nonparametric estimators for the tail copulae are introduced and weak convergence, asymptotic normality, and strong consistency are shown by means of a functional delta-method. Further, weak convergence of a general upper-order rank-statistics for extreme events is investigated and the relationship to tail dependence is provided. A simulation study compares the introduced estimators and two financial data sets are analyzed with our methods. 1

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@inproceedings{Schmidt2004NonparametricEO, title={Nonparametric estimation of tail dependence}, author={Rafael Schmidt and Ulrich Stadtm{\"{u}ller}, year={2004} }