Related papers: Extremes for stationary regularly varying random f…
Let $X(t), t\in \mathcal{T}$ be a centered Gaussian random field with variance function $\sigma^2(\cdot)$ that attains its maximum at the unique point $t_0\in \mathcal{T}$, and let $M(\mathcal{T}):=\sup_{t\in \mathcal{T}} X(t)$. For…
The risk of catastrophes is related to the possibility of occurring extreme values. Several statistical methodologies have been developed in order to evaluate the propensity of a process for the occurrence of high values and the permanence…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
We develop an asymptotic theory for extremes in decomposable graphical models by presenting results applicable to a range of extremal dependence types. Specifically, we investigate the weak limit of the distribution of suitably normalised…
Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical…
To draw inference on serial extremal dependence within heavy-tailed Markov chains, Drees, Segers and Warcho{\l} [Extremes (2015) 18, 369--402] proposed nonparametric estimators of the spectral tail process. The methodology can be extended…
We study a new estimator for the tail index of a distribution in the Frechet domain of attraction that arises naturally by computing subsample maxima. This estimator is equivalent to taking a U-statistic over a Hill estimator with two order…
Two old conjectures from problem sections, one of which from SIAM Review, concern the question of finding distributions that maximize P(Sn <= t), where Sn is the sum of i.i.d. random variables X1, ..., Xn on the interval [0,1], satisfying…
The task for a general and useful classification of the tail behaviors of probability distributions still has no satisfactory solution. Due to lack of information outside the range of the data the tails of the distribution should be…
Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
We develop a probabilistic method for assessing the tail behavior and geometric stability of one-dimensional n i.i.d. samples by tracking how their span contracts when the most extreme points are trimmed. Central to our approach is the…
We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an…
We consider empirical multi-dimensional Rare Events Point Processes that keep track both of the time occurrence of extremal observations and of their severity, for stochastic processes arising from a dynamical system, by evaluating a given…
Clustering of extreme events can have profound and detrimental societal consequences. The extremal index, a number in the unit interval, is a key parameter in modelling the clustering of extremes. The study of extremal index often assumes a…
Regular variation provides a convenient theoretical framework to study large events. In the multivariate setting, the dependence structure of the positive extremes is characterized by a measure - the spectral measure - defined on the…
We use extreme value theory to estimate the probability of successive exceedances of a threshold value of a time-series of an observable on several classes of chaotic dynamical systems. The observables have either a Fr\'echet (fat-tailed)…
This paper establishes asymptotic results for the maximum likelihood and restricted maximum likelihood (REML) estimators of the parameters in the nested error regression model for clustered data when both of the number of independent…