In the sixties Mandelbrot already showed that extreme price swings are more likely than some of us think or incorporate in our models. A modern toolbox for analyzing such rare events can be found in the field of extreme value theory. At the core of extreme value theory lies the modelling of...

Classical extreme-value theory for stationary sequences of random variables can up to a large extent be paraphrased as the study of exceedances over a high threshold. A special role within the description of the temporal dependence between such exceedances is played by the extremal index. Parts...

We establish Edgeworth expansions for the distribution function of the centered and normalized Hill estimator for the reciprocal of the index of regular variation of the tail of a distribution function.The expansions are used to derive expansions for coverage probabilities of confidence...

For multivariate distributions in the domain of attraction of a max-stable distribution, the tail copula and the stable tail dependence function are equivalent ways to capture the dependence in the upper tail. The empirical versions of these functions are rank-based estimators whose inflated...

Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models such as those arising from recent max-linear structural equation models. Moreover, they can be hard to compute in higher dimensions. An adaptive...

Tail dependence models for distributions attracted to a max-stable law are fitted using observations above a high threshold. To cope with spatial, high-dimensional data, a rank based M-estimator is proposed relying on bivariate margins only. A data-driven weight matrix is used to minimize the...