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The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…

Methodology · Statistics 2025-05-05 Emma S. Simpson , Jonathan A. Tawn

We propose a new class of estimators for Pickands dependence function which is based on the concept of minimum distance estimation. An explicit integral representation of the function $A^*(t)$, which minimizes a weighted $L^2$-distance…

Statistics Theory · Mathematics 2015-03-18 Axel Bücher , Holger Dette , Stanislav Volgushev

Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent.…

Methodology · Statistics 2015-10-30 Jennifer Wadsworth , Jonathan Tawn , Anthony Davison , Daniel Elton

The distribution of block maxima of sequences of independent and identically-distributed random variables is used to model extreme values in many disciplines. The traditional extreme value (EV) theory derives a closed-form expression for…

Methodology · Statistics 2019-02-27 Marco Marani , Enrico Zorzetto

It is well known that an extreme order statistic and a central order statistic (os) as well as an intermediate os and a central os from a sample of iid univariate random variables get asymptotically independent as the sample size increases.…

Statistics Theory · Mathematics 2017-02-01 Michael Falk , Florian Wisheckel

We use the framework of multivariate regular variation to analyse the extremal behaviour of preferential attachment models. To this end, we follow a directed linear preferential attachment model for a random, heavy-tailed number of steps in…

Probability · Mathematics 2024-08-06 Anja Janßen , Max Ziegenbalg

Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…

Methodology · Statistics 2026-01-15 Nisrine Madhar , Juliette Legrand , Maud Thomas

The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…

Methodology · Statistics 2012-09-28 Soyoung Jeon , Richard L. Smith

This work proposes an estimator with both Peak-Over-Threshold and Block-Maxima flavors, uses it to estimate the Pickands dependence function of bivariate time series, and illustrates how it brings down the asymptotic bias and the overall…

Methodology · Statistics 2022-02-15 Nan Zou

The empirical copula process plays a central role in the asymptotic analysis of many statistical procedures which are based on copulas or ranks. Among other applications, results regarding its weak convergence can be used to develop…

Statistics Theory · Mathematics 2014-11-24 Axel Bücher , Betina Berghaus , Stanislav Volgushev

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

Understanding variable dependence, particularly eliciting their statistical properties given a set of covariates, provides the mathematical foundation in practical operations management such as risk analysis and decision-making given…

Methodology · Statistics 2023-09-06 Yunyun Wang , Tatsushi Oka , Dan Zhu

The present article is devoted to the semi-parametric estimation of multivariate expectiles for extreme levels. The considered multivariate risk measures also include the possible conditioning with respect to a functional covariate,…

Statistics Theory · Mathematics 2023-03-30 Elena Di Bernardino , Thomas Laloë , Cambyse Pakzad

The probabilistic characterization of the relationship between two or more random variables calls for a notion of dependence. Dependence modeling leads to mathematical and statistical challenges, and recent developments in extremal…

Methodology · Statistics 2025-03-11 Giovanni Puccetti , Ruodu Wang

For a bivariate random vector (X,Y), symmetry conditions are presented that yield stochastic orderings among |X|, |Y|, |max(X,Y)|, and | min(X, Y)|. Partial extensions of these results for multivariate random vectors (X1,...,Xn) are also…

Statistics Theory · Mathematics 2012-06-22 Yindeng Jiang , Michael D. Perlman

In this paper we improve some existing results concerning the approximation of the distribution of extremes of a 1-dependent and stationary sequence of random variables. We enlarge the range of applicability and improve the approximation…

Probability · Mathematics 2012-11-26 Alexandru Amarioarei

The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…

Statistics Theory · Mathematics 2015-05-11 Helena Ferreira , Marta Ferreira

The angular measure on the unit sphere characterizes the first-order dependence structure of the components of a random vector in extreme regions and is defined in terms of standardized margins. Its statistical recovery is an important step…

Statistics Theory · Mathematics 2024-07-16 Stéphane Lhaut , Johan Segers

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

This paper provides a characterization of all possible dependency structures between two stochastically ordered random variables. The answer is given in terms of copulas that are compatible with the stochastic order and the marginal…

Probability · Mathematics 2019-12-16 Sebastian Arnold , Ilya Molchanov , Johanna F. Ziegel