Related papers: Linking representations for multivariate extremes …
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…
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…
Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise…
From environmental sciences to finance, there is a growing demand for methods that can assess the risks of extreme events beyond those observed in available data. Extrapolating extreme events beyond the range of the data is not obvious.…
We attempt to bring some modest unity to three subareas of heavy tail analysis and extreme value theory: limit laws for componentwise maxima of iid random variables;hidden regular variation and asymptotic independence;conditioned limit laws…
We consider stationary sequences whose marginal tail is subexponential and lies in the Gumbel Maximum domain of attraction. Due to the extremely strong dependence, their extreme values are caused by multiple big values and are clustered in…
Extremal graphical models are sparse statistical models for multivariate extreme events. The underlying graph encodes conditional independencies and enables a visual interpretation of the complex extremal dependence structure. For the…
Determining the causes of extreme events is a fundamental question in many scientific fields. An important aspect when modelling multivariate extremes is the tail dependence. In application, the extreme dependence structure may…
Data exhibiting heavy-tails in one or more dimensions is often studied using the framework of regular variation. In a multivariate setting this requires identifying specific forms of dependence in the data; this means identifying that the…
We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the…
Capturing the dependence structure of multivariate extreme events is a major concern in many fields involving the management of risks stemming from multiple sources, e.g. portfolio monitoring, insurance, environmental risk management and…
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,…
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…
Extremal graphical models encode the conditional independence structure of multivariate extremes. Key statistics for learning extremal graphical structures are empirical extremal variograms, for which we prove non-asymptotic concentration…
Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
This paper unifies and extends results on a class of multivariate Extreme Value (EV) models studied by Hougaard, Crowder, and Tawn. In these models both unconditional and conditional distributions are EV, and all lower-dimensional marginals…
In this paper extremal values of the difference between several graph invariants related to the metric dimension are studied: mixed metric dimension, edge metric dimension and strong metric dimension. These non-trivial extremal values are…
Several environmental phenomena can be described by different correlated variables that must be considered jointly in order to be more representative of the nature of these phenomena. For such events, identification of extremes is…
Recursive max-linear vectors provide models for causal dependence between large values of random variables that are supported on directed acyclic graphs, but the standard assumption that all nodes of such a graph are observed can be…