相关论文: On the spatial extent of extreme threshold exceeda…
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. For statistical inference it is often assumed that…
Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way…
Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…
The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees, Segers and Warchol [Extremes 18(3): 369--402, 2015] proposed estimators of the marginal distributions of this…
In this paper, we analyze the asymptotic behavior of the point process of exceedances in a spatio-temporal setting whose points are given by the rescaled occurrence times, the sites and the rescaled values of exceedances. Here, the…
Predicting extreme events in nonlinear dynamical systems is challenging due to a limited understanding of their statistical properties. This study numerically and theoretically investigates the statistical properties of infinite-modal maps…
It is no secret that statistical modelling often involves making simplifying assumptions when attempting to study complex stochastic phenomena. Spatial modelling of extreme values is no exception, with one of the most common such…
In this study, spatial stochastic and logistic model (SSLM) describing dynamics of a population of a certain species was analysed. The behaviour of the extinction threshold as a function of model parameters was studied. More specifically,…
Extreme events are unusual and rare large-amplitude fluctuations that occur can unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize…
Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these…
Models for extreme values are generally derived from limit results, which are meant to be good enough approximations when applied to finite samples. Depending on the speed of convergence of the process underlying the data, these…
Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an…
We consider extremal eigenvalues of sparse random matrices, a class of random matrices including the adjacency matrices of Erd\H{o}s-R\'{e}nyi graphs $\mathcal{G}(N,p)$. Recently, it was shown that the leading order fluctuations of extremal…
The goal of this paper is two-fold: 1. We review classical and recent measures of serial extremal dependence in a strictly stationary time series as well as their estimation. 2. We discuss recent concepts of heavy-tailed time series,…
We investigate Lipschitz-Killing curvatures for excursion sets of random fields on $\mathbb R^2$ under small spatial-invariant random perturbations. An expansion formula for mean curvatures is derived when the magnitude of the perturbation…
When considering d possibly dependent random variables, one is often interested in extreme risk regions, with very small probability p. We consider risk regions of the form ${\mathbf{z}\in\mathbb{R}^d:f(\mathbf{z})\leq\beta}$, where f is…
We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.
The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…
The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to…
Conditional independence, graphical models and sparsity are key notions for parsimonious statistical models and for understanding the structural relationships in the data. The theory of multivariate and spatial extremes describes the risk…