Related papers: Analysis of extreme values with random location
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…
This paper devises a regression-type model for the situation where both the response and covariates are extreme. The proposed approach is designed for the setting where both the response and covariates are themselves block maxima, and thus…
We study distributional robustness in the context of Extreme Value Theory (EVT). We provide a data-driven method for estimating extreme quantiles in a manner that is robust against incorrect model assumptions underlying the application of…
This paper introduces a novel sub-sampling block maxima technique to model and characterize environmental extreme risks. We examine the relationships between block size and block maxima statistics derived from the Gaussian and generalized…
In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…
In extreme value theory, there are two fundamental approaches, both widely used: the block maxima (BM) method and the peaks-over-threshold (POT) method. Whereas much theoretical research has gone into the POT method, the BM method has not…
In financial markets marked by inherent volatility, extreme events can result in substantial investor losses. This paper proposes a portfolio strategy designed to mitigate extremal risks. By applying extreme value theory, we evaluate the…
Extreme value theory is concerned with probabilistic and statistical questions related to very high or very low values in sequences of random variables and in stochastic processes. The subject has a rich mathematical theory and also a long…
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…
Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max-stable…
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…
A coupling method is developed for univariate extreme value theory , providing an alternative to the use of the tail empirical/quantile processes. Emphasizing the Peak-over-Threshold approach that approximates the distribution above high…
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.…
The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…
Quantile regression is a statistical method which, unlike classical regression, aims to predict the conditional quantiles. Classical quantile regression methods face difficulties, particularly when the quantile under consideration is…
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…
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that,…
The block maxima (BM) approach in extreme value analysis fits a sample of block maxima to the Generalized Extreme Value (GEV) distribution. We consider all potential blocks from a sample, which leads to the All Block Maxima (ABM) estimator.…
Block maxima methods constitute a fundamental part of the statistical toolbox in extreme value analysis. However, most of the corresponding theory is derived under the simplifying assumption that block maxima are independent observations…
In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…