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Davis and Mikosch [7] introduced the extremogram as a flexible quantitative tool for measuring various types of extremal dependence in a stationary time series. There we showed some standard statistical properties of the sample extremogram.…

Methodology · Statistics 2011-07-29 Richard A. Davis , Thomas Mikosch , Ivor Cribben

The risk of catastrophes is related to the possibility of occurring extreme values. Several statistical methodologies have been developed in order to evaluate the propensity of a process for the occurrence of high values and the permanence…

Statistics Theory · Mathematics 2019-05-08 Helena Ferreira , Marta Ferreira

In this paper we characterize the limiting behavior of sums of extreme values of long range dependent sequences defined as functionals of linear processes with finite variance. The extremal sums behave completely different by compared to…

Probability · Mathematics 2007-06-13 Rafal Kulik

In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take…

Methodology · Statistics 2022-07-19 Emma S. Simpson , Jennifer L. Wadsworth , Jonathan A. Tawn

Factor models have large potencial in the modeling of several natural and human phenomena. In this paper we consider a multivariate time series $\mb{Y}_n$, ${n\geq 1}$, rescaled through random factors $\mb{T}_n$, ${n\geq 1}$, extending some…

Probability · Mathematics 2013-06-18 Helena Ferreira , Marta Ferreira

The upcrossings index $0\leq \eta\leq 1,$ a measure of the degree of local dependence in the upcrossings of a high level by a stationary process, plays, together with the extremal index $\theta,$ an important role in extreme events…

Probability · Mathematics 2015-08-04 Ana Paula Martins , João Renato Sebastião

One of the main topics of extreme value analysis is to estimate the extreme value index, an important parameter that controls the tail behavior of the distribution. In many cases, estimating the extreme value index of the target variable…

Methodology · Statistics 2024-10-22 Takuma Yoshida , Yuta Umezu

Some problems of statistics can be reduced to extremal problems of minimizing functionals of smooth functions defined on the cube $[0,1]^m$, $m\geq 2$. In this paper, we study a class of extremal problems that is closely connected to the…

Probability · Mathematics 2010-12-06 Alexander Nazarov , Natalia Stepanova

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

Let $\{X_{\mathbf{n}} : \mathbf{n}\in\mathbb{Z}^d\}$ be a weakly dependent stationary field with maxima $M_{A} := \sup\{X_{\mathbf{i}} : \mathbf{i}\in A\}$ for finite $A\subset\mathbb{Z}^d$ and $M_{\mathbf{n}} := \sup\{X_{\mathbf{i}} :…

Probability · Mathematics 2019-08-20 Natalia Soja-Kukieła

Statistical methods for inference on spatial extremes of large datasets are yet to be developed. Motivated by standard dimension reduction techniques used in spatial statistics, we propose an approach based on empirical basis functions to…

Methodology · Statistics 2018-08-02 Samuel A. Morris , Brian J. Reich , Emeric Thibaud

Any limiting point process for the time normalized exceedances of high levels by a stationary sequence is necessarily compound Poisson under appropriate long range dependence conditions. Typically exceedances appear in clusters. The…

Applications · Statistics 2009-03-03 Christian Y. Robert

Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…

Methodology · Statistics 2021-06-08 Shreyan Ganguly , Peter F. Craigmile

We obtain an almost sure bound for oscillation rates of empirical distribution functions for stationary causal processes. For short-range dependent processes, the oscillation rate is shown to be optimal in the sense that it is as sharp as…

Probability · Mathematics 2007-05-23 Wei Biao Wu

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…

Applications · Statistics 2021-03-16 Whitney K. Huang , Adam H. Monahan , Francis W. Zwiers

We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…

Methodology · Statistics 2015-02-26 Rafał Kulik , Zhigang Tong

A measure of primal importance for capturing the serial dependence of a stationary time series at extreme levels is provided by the limiting cluster size distribution. New estimators based on a blocks declustering scheme are proposed and…

Statistics Theory · Mathematics 2020-11-11 Axel Bücher , Tobias Jennessen

We consider the clustering of extremes for stationary regularly varying random fields over arbitrary growing index sets. We study sufficient assumptions on the index set such that the limit of the point random fields of the exceedances…

Probability · Mathematics 2022-02-23 Riccardo Passeggeri , Olivier Wintenberger

Heavy tailed phenomena are naturally analyzed by extreme value statistics. A crucial step in such an analysis is the estimation of the extreme value index, which describes the tail heaviness of the underlying probability distribution. We…

Statistics Theory · Mathematics 2018-07-18 Hanan Ahmed , John H. J. Einmahl

We propose a spectral clustering algorithm for analyzing the dependence structure of multivariate extremes. More specifically, we focus on the asymptotic dependence of multivariate extremes characterized by the angular or spectral measure…

Machine Learning · Statistics 2023-08-02 Marco Avella Medina , Richard A. Davis , Gennady Samorodnitsky