Related papers: Markov Kernels and the Conditional Extreme Value M…
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…
We investigate conditions for the existence of the limiting conditional distribution of a bivariate random vector when one component becomes large. We revisit the existing literature on the topic, and present some new sufficient conditions.…
Extreme value theory for univariate and low-dimensional observations has been explored in considerable detail, but the field is still in an early stage regarding high-dimensional settings. This paper focuses on H\"usler-Reiss models, a…
The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…
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…
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…
We investigate extreme values of Mahonian and Eulerian distributions arising from counting inversions and descents of random elements of finite Coxeter groups. To this end, we construct a triangular array of either distribution from a…
Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial…
Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…
Quantile regression is an increasingly important empirical tool in economics and other sciences for analyzing the impact of a set of regressors on the conditional distribution of an outcome. Extremal quantile regression, or quantile…
We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic…
This note compares two approaches both alternatively used when establishing normality theorems in univariate Extreme Value Theory. When the underlying distribution function ($df$) is the extremal domain of attraction, it is possible to use…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
Simultaneous concurrence of extreme values across multiple climate variables can result in large societal and environmental impacts. Therefore, there is growing interest in understanding these concurrent extremes. In many applications, not…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
In this paper we introduce and study the class of multivariate strong and strongly subexponential distributions. Some first properties are verified, as for example a type of multivariate analogue of Kesten's inequality, the closure property…
The masses of data now available have opened up the prospect of discovering weak signals using machine-learning algorithms, with a view to predictive or interpretation tasks. As this survey of recent results attempts to show, bringing…
Statistical extreme value theory is concerned with the use of asymptotically motivated models to describe the extreme values of a process. A number of commonly used models are valid for observed data that exceed some high threshold.…
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
Max-stable random fields play a central role in modeling extreme value phenomena. We obtain an explicit formula for the conditional probability in general max-linear models, which include a large class of max-stable random fields. As a…