相关论文: On generalized max-linear models and their statist…

In practice, it is not possible to observe a whole max-stable random field. Therefore, a way how to reconstruct a max-stable random field in $C\left([0,1]^k\right)$ by interpolating its realizations at finitely many points is proposed. The…

Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…

The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…

Max-stable processes play an important role as models for spatial extreme events. Their complex structure as the pointwise maximum over an infinite number of random functions makes simulation highly nontrivial. Algorithms based on finite…

We consider the random field M(t)=\sup_{n\geq 1}\big\{-\log A_{n}+X_{n}(t)\big\}\,,\qquad t\in T\, for a set $T\subset \mathbb{R}^{m}$, where $(X_{n})$ is an iid sequence of centered Gaussian random fields on $T$ and $0<A_{1}<A_{2}<\cdots $…

Max-stable processes provide natural models for the modelling of spatial extreme values observed at a set of spatial sites. Full likelihood inference for max-stable data is, however, complicated by the form of the likelihood function as it…

We address the notion of association of sum- and max- stable processes from the perspective of linear and max-linear isometries. We establish the appealing results that these two classes of isometries can be identified on a proper space…

We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation algorithm, which combines statistical and computational efficiency in high-dimensions.…

With any max-stable random process $\eta$ on $\mathcal{X}=\mathbb{Z}^d$ or $\mathbb{R}^d$, we associate a random tessellation of the parameter space $\mathcal{X}$. The construction relies on the Poisson point process representation of the…

We develop classification results for max--stable processes, based on their spectral representations. The structure of max--linear isometries and minimal spectral representations play important roles. We propose a general classification…

Max-stable random sketches can be computed efficiently on fast streaming positive data sets by using only sequential access to the data. They can be used to answer point and Lp-norm queries for the signal. There is an intriguing connection…

Consider the max-stable process $\eta(t) = \max_{i\in\mathbb N} U_i \rm{e}^{\langle X_i, t\rangle - \kappa(t)}$, $t\in\mathbb{R}^d$, where $\{U_i, i\in\mathbb{N}\}$ are points of the Poisson process with intensity $u^{-2}\rm{d} u$ on…

Max-stable random fields provide canonical models for the dependence of multivariate extremes. Inference with such models has been challenging due to the lack of tractable likelihoods. In contrast, the finite dimensional cumulative…

Aulbach et al. (2013) introduced a max-domain of attraction approach for extreme value theory in C[0,1] based on functional distribution functions, which is more general than the approach based on weak convergence in de Haan and Lin (2001).…

This paper deals with the question of conditional sampling and prediction for the class of stationary max-stable processes which allow for a mixed moving maxima representation. We develop an exact procedure for conditional sampling using…

Max-stable processes are widely used to model spatial extremes. These processes exhibit asymptotic dependence meaning that the large values of the process can occur simultaneously over space. Recently, inverted max-stable processes have…

Multivariate extreme-value analysis is concerned with the extremes in a multivariate random sample, that is, points of which at least some components have exceptionally large values. Mathematical theory suggests the use of max-stable models…

Being the max-analogue of $\alpha$-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the…

In extreme value statistics, the peaks-over-threshold method is widely used. The method is based on the generalized Pareto distribution characterizing probabilities of exceedances over high thresholds in $\mathbb {R}^d$. We present a…

Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…