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Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such processes we propose a two-step parameter estimation of the extremogram, when some part of the domain…

Statistics Theory · Mathematics 2018-08-28 Sven Buhl , Claudia Klüppelberg

Moving average processes driven by exponential-tailed L\'evy noise are important extensions of their Gaussian counterparts in order to capture deviations from Gaussianity, more flexible dependence structures, and sample paths with jumps.…

Statistics Theory · Mathematics 2023-08-01 Zhongwei Zhang , David Bolin , Sebastian Engelke , Raphaël Huser

A network evolution with predicted tail and extremal indices of PageRank and the Max-Linear Model used as node influence indices in random graphs is considered. The tail index shows a heaviness of the distribution tail. The extremal index…

Statistics Theory · Mathematics 2022-11-28 Natalia Markovich

Consider the max-stable process $\eta(t) = \max_{i\in\mathbb N} U_i \rm{e}^{\langle X_i, t\rangle - \kappa(t)}$, $t\in\mathbb{R}^d$, where $\{U_i, i\in\mathbb{N}\}$ are points of the Poisson process with intensity $u^{-2}\rm{d} u$ on…

Probability · Mathematics 2015-12-09 Sebastian Engelke , Zakhar Kabluchko

Max-stable processes have proved to be useful for the statistical modelling of spatial extremes. Several representations of max-stable random fields have been proposed in the literature. One such representation is based on a limit of…

Methodology · Statistics 2012-04-26 Richard A. Davis , Claudia Klüppelberg , Christina Steinkohl

Understanding the nuanced performance of machine learning models is essential for responsible deployment, especially in high-stakes domains like healthcare and finance. This paper introduces a novel framework, Conformalized Exceptional…

Machine Learning · Computer Science 2025-08-22 Xin Du , Sikun Yang , Wouter Duivesteijn , Mykola Pechenizkiy

Extreme events are a major concern in statistical modeling. Ran\-dom missing data can constitute a problem when modeling such rare events. Imputation is crucial in these situations and therefore models that describe different imputation…

Probability · Mathematics 2020-02-10 Helena Ferreira , Ana Paula Martins , Maria da Graça Temido

There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…

Probability · Mathematics 2022-12-05 Anja Janßen , Sebastian Neblung , Stilian Stoev

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,…

Statistics Theory · Mathematics 2013-03-27 Richard A. Davis , Thomas Mikosch , Yuwei Zhao

The stable-regenerative multiple-stable model has been shown recently to have distinct candidate extremal index and extremal index. To understand further this rare phenomenon, two more results are established here for the double-stable…

Probability · Mathematics 2024-10-10 Shuyang Bai , Rafał Kulik , Yizao Wang

We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its…

Probability · Mathematics 2022-11-09 Lanpeng Ji , Xiaofan Peng

The maximum entropy ansatz, as it is often invoked in the context of time-series analysis, suggests the selection of a power spectrum which is consistent with autocorrelation data and corresponds to a random process least predictable from…

Probability · Mathematics 2008-07-19 Tryphon T. Georgiou

We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed points and prove the existence of Extreme Value Laws for such processes. We use an approach developed in \cite{FFV16},…

Dynamical Systems · Mathematics 2017-07-17 Ana Cristina Moreira Freitas , Jorge Milhazes Freitas , Sandro Vaienti

We study the Wiener--Hopf factorization and the distribution of extrema for general stable processes. By connecting the Wiener--Hopf factors with a certain elliptic-like function we are able to obtain many explicit and general results, such…

Probability · Mathematics 2011-04-11 Alexey Kuznetsov

Max-affine regression refers to a model where the unknown regression function is modeled as a maximum of $k$ unknown affine functions for a fixed $k \geq 1$. This generalizes linear regression and (real) phase retrieval, and is closely…

Machine Learning · Statistics 2019-06-24 Avishek Ghosh , Ashwin Pananjady , Adityanand Guntuboyina , Kannan Ramchandran

We consider a stationary stochastic volatility field $Y_vZ_v$ with $v\in\mathbb{Z}^d$, where $Z$ is regularly varying and $Y$ has lighter tails and is independent of $Z$. We make - relative to existing literature - very general assumptions…

Probability · Mathematics 2023-01-25 Mads Stehr , Anders Rønn-Nielsen

We consider stationary configurations of points in Euclidean space which are marked by positive random variables called scores. The scores are allowed to depend on the relative positions of other points and outside sources of randomness.…

Probability · Mathematics 2025-06-25 Bojan Basrak , Ilya Molchanov , Hrvoje Planinić

The estimation of categorical distributions under marginal constraints summarizing some sample from a population in the most-generalizable way is key for many machine-learning and data-driven approaches. We provide a parameter-agnostic…

High Energy Physics - Theory · Physics 2023-11-17 Orestis Loukas , Ho Ryun Chung

In this paper, we establish limit theorems for the supremum of the support, denoted by $M_t$, of a supercritical super-Brownian motion $\{X_t, t\ge0\}$ on $\mathbb{R}$. We prove that there exists an $m(t)$ such that $(X_t-m(t), M_t-m(t))$…

Probability · Mathematics 2020-11-04 Yan-Xia Ren , Renming Song , Rui Zhang

In recent years, parametric models for max-stable processes have become a popular choice for modeling spatial extremes because they arise as the asymptotic limit of rescaled maxima of independent and identically distributed random…

Methodology · Statistics 2025-05-14 Carolin Forster , Marco Oesting