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We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…

Probability · Mathematics 2016-09-08 Henrik Hult , Sandeep Juneja , Karthyek Murthy

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…

Probability · Mathematics 2009-09-29 Sidney I. Resnick

We introduce the extremal range, a local statistic for studying the spatial extent of extreme events in random fields on $\mathbb{R}^d$. Conditioned on exceedance of a high threshold at a location $s$, the extremal range at $s$ is the…

Statistics Theory · Mathematics 2024-11-06 Ryan Cotsakis , Elena Di Bernardino , Thomas Opitz

In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…

Probability · Mathematics 2014-07-04 Jeffrey F. Collamore , Guoqing Diao , Anand N. Vidyashankar

We propose a method for high dimensional multivariate regression that is robust to random error distributions that are heavy-tailed or contain outliers, while preserving estimation accuracy in normal random error distributions. We extend…

Methodology · Statistics 2025-03-05 Mayu Hiraishi , Kensuke Tanioka , Hiroshi Yadohisa

Risk measures such as Conditional Value-at-Risk (CVaR) focus on extreme losses, where scarce tail data makes model error unavoidable. To hedge misspecification, one evaluates worst-case tail risk over an ambiguity set. Using Extreme Value…

Risk Management · Quantitative Finance 2026-01-22 Anand Deo

The estimation of the extremal dependence structure is spoiled by the impact of the bias, which increases with the number of observations used for the estimation. Already known in the univariate setting, the bias correction procedure is…

Statistics Theory · Mathematics 2015-04-03 Anne-Laure Fougères , Laurens de Haan , Cécile Mercadier

Variational inference has been widely used in machine learning literature to fit various Bayesian models. In network analysis, this method has been successfully applied to solve the community detection problems. Although these results are…

Machine Learning · Statistics 2024-05-22 Xuezhen Li , Can M. Le

The tail chain of a Markov chain can be used to model the dependence between extreme observations. For a positive recurrent Markov chain, the tail chain aids in describing the limit of a sequence of point processes $\{N_n,n\geq1\}$,…

Statistics Theory · Mathematics 2013-10-01 Sidney I. Resnick , David Zeber

The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based…

Methodology · Statistics 2012-04-17 Miguel de Carvalho , Boris Oumow , Johan Segers , Michał Warchoł

Analysis of the rare and extreme values through statistical modeling is an important issue in economical crises, climate forecasting, and risk management of financial portfolios. Extreme value theory provides the probability models needed…

Methodology · Statistics 2017-02-15 Ali Reza Fotouhi

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…

Statistics Theory · Mathematics 2019-02-20 Thomas Lugrin , Anthony C. Davison , Jonathan A. Tawn

A novel and comprehensive methodology designed to tackle the challenges posed by extreme values in the context of random censorship is introduced. The main focus is on the analysis of integrals based on the product-limit estimator of…

Statistics Theory · Mathematics 2025-02-18 Martin Bladt , Igor Rodionov

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…

Methodology · Statistics 2024-12-25 Shuang Hu , Zuoxiang Peng , Johan Segers

We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…

Dynamical Systems · Mathematics 2026-01-21 Romain Aimino , Ana Cristina Moreira Freitas , Jorge Milhazes Freitas , Mike Todd

The EVA 2023 data competition consisted of four challenges, ranging from interval estimation for very high quantiles of univariate extremes conditional on covariates, point estimation of unconditional return levels under a custom loss…

Applications · Statistics 2023-12-22 Léo R. Belzile , Arnab Hazra , Rishikesh Yadav

Extremes play a special role in Anomaly Detection. Beyond inference and simulation purposes, probabilistic tools borrowed from Extreme Value Theory (EVT), such as the angular measure, can also be used to design novel statistical learning…

Machine Learning · Statistics 2016-04-01 Nicolas Goix , Anne Sabourin , Stéphan Clémençon

The goal in extreme multi-label classification is to learn a classifier which can assign a small subset of relevant labels to an instance from an extremely large set of target labels. Datasets in extreme classification exhibit a long tail…

Machine Learning · Statistics 2018-03-06 Rohit Babbar , Bernhard Schölkopf

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…

Statistics Theory · Mathematics 2021-08-17 Natalia Nolde , Jennifer L. Wadsworth

Consider two stationary time series with heavy-tailed marginal distributions. We aim to detect whether they have a causal relation, that is, if a change in one causes a change in the other. Usual methods for causal discovery are not well…

Statistics Theory · Mathematics 2023-11-20 Juraj Bodik , Zbyněk Pawlas , Milan Paluš