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The tail process revisited
The tail measure of a regularly varying stationary time series has been recently introduced. It is used in this contribution to reconsider certain...
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Second-order Asymptotics on Distributions of Maxima of Bivariate Elliptical Arrays
Let {( ξ ni , η ni ), 1 ≤ i ≤ n , n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function...
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Fitting phase–type scale mixtures to heavy–tailed data and distributions
We consider the fitting of heavy tailed data and distributions with a special attention to distributions with a non–standard shape in the “body” of...
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Prediction of catastrophes in space over time
Predicting rare events, such as high level up-crossings, for spatio-temporal processes plays an important role in the analysis of the occurrence and...
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Threshold selection for multivariate heavy-tailed data
Regular variation is often used as the starting point for modeling multivariate heavy-tailed data. A random vector is regularly varying if and only...
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On the tail behavior of a class of multivariate conditionally heteroskedastic processes
Conditions for geometric ergodicity of multivariate autoregressive conditional heteroskedasticity (ARCH) processes, with the so-called BEKK (Baba,...
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Emil J. Gumbel’s last course on the “Statistical theory of extreme values”: a conversation with Tuncel M. Yegulalp
GUMBEL. Eponym in mathematical statistics for the first type extreme value distribution and the copula that is both of extreme value and Archimedean...
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Coupled Continuous Time Random Maxima
Continuous Time Random Maxima (CTRM) are a generalization of classical extreme value theory: Instead of observing random events at regular intervals...
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Maximum loss and maximum gain of spectrally negative Lévy processes
The joint distribution of the maximum loss and the maximum gain is obtained for a spectrally negative Lévy process until the passage time of a given...
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Tail Approximations for Sums of Dependent Regularly Varying Random Variables Under Archimedean Copula Models
In this paper, we compare two numerical methods for approximating the probability that the sum of dependent regularly varying random variables...
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Asymptotic normality of the likelihood moment estimators for a stationary linear process with heavy-tailed innovations
The authors recently proved in Martig and Hüsler (
2016 ) that the likelihood moment estimators are consistent estimators for the parameters of the... -
Densities of Ruin-Related Quantities in the Cramér-Lundberg Model with Pareto Claims
In this paper, we consider the classical yet widely applicable Cramér-Lundberg risk model with Pareto distributed claim sizes. Building on the...
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Asymptotics for the partial sum and its maximum of dependent random variables*
Let X 1 ,…, X n be pairwise asymptotically independent or pairwise upper extended negatively dependent real-valued random variables. Under the...
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A continuous updating weighted least squares estimator of tail dependence in high dimensions
Likelihood-based procedures are a common way to estimate tail dependence parameters. They are not applicable, however, in non-differentiable models...
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Precise large deviations for sums of random vectors with dependent components of consistently varying tails
Let {
X i = ( X 1, i ,..., X m,i ) ⊤ , i ≥ 1} be a sequence of independent and identically distributed nonnegative m -dimensional random vectors. The... -
Regular variation of a random length sequence of random variables and application to risk assessment
When assessing risks on a finite-time horizon, the problem can often be reduced to the study of a random sequence C ( N ) = ( C 1 ,…, C N ) of random length