Related papers: The coupling method in extreme value theory
When modeling a vector of risk variables, extreme scenarios are often of special interest. The peaks-over-thresholds method hinges on the notion that, asymptotically, the excesses over a vector of high thresholds follow a multivariate…
We theoretically and numerically investigated the threshold network model with a generic weight function where there were a large number of nodes and a high threshold. Our analysis was based on extreme value theory, which gave us a…
Peaks-over-threshold analysis using the generalized Pareto distribution is widely applied in modelling tails of univariate random variables, but much information may be lost when complex extreme events are studied using univariate results.…
Panel data arise in a wide range of application areas, and developing modelling methods for extreme values under such a setup is essential for reliable risk assessment and management. When choosing to model the marginal distributions of…
Multivariate peaks over thresholds modeling based on generalized Pareto distributions has up to now only been used in few and mostly 2-dimensional situations. This paper contributes theoretical understanding, physically based models,…
A method is described for predicting extremes values beyond the span of historical data. The method - based on extending a curve fitted to a location- and scale-invariant variation of the double-logarithmic QQ-plot - is simple and…
When assessing the impact of extreme events, it is often not just a single component, but the combined behaviour of several components which is important. Statistical modelling using multivariate generalized Pareto (GP) distributions…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
Recently attention has been drawn to practical problems with the use of unbounded Pareto distributions, for instance when there are natural upper bounds that truncate the probability tail. Aban, Meerschaert and Panorska (2006) derived the…
We study random circle maps that are expanding on the average. Uniform bounds on neither expansion nor distortion are required. We construct a coupling scheme, which leads to exponential convergence of measures (memory loss) and exponential…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…
Extreme value theory offers a statistical framework for quantifying the risk of rare events, with the generalized Pareto (GP) distribution providing the canonical limit model for univariate threshold exceedances. In many applications,…
A tail empirical process for heavy-tailed and right-censored data is introduced and its Gaussian approximation is established. In this context, a (weighted) new Hill-type estimator for positive extreme value index is proposed and its…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a "meta-stable set." In the example of the…
The statistical modeling of discrete extremes has received less attention than their continuous counterparts in the Extreme Value Theory (EVT) literature. One approach to the transition from continuous to discrete extremes is the modeling…
In this paper, we establish sharp upper and lower bounds on the convergence rate of the empirical measures of point processes under the Wasserstein distance. To this end, we first introduce a new metric on the space of counting measures…
We review some recent development in the theory of spatial extremes related to Pareto Processes and modeling of threshold exceedances. We provide theoretical background, methodology for modeling, simulation and inference as well as an…