• Extremes (IF 1.136) Pub Date : 2020-07-27
B. Beranger, A. G. Stephenson, S. A. Sisson

Max-stable processes are a popular tool for the study of environmental extremes, and the extremal skew-t process is a general model that allows for a flexible extremal dependence structure. For inference on max-stable processes with high-dimensional data, exact likelihood-based estimation is computationally intractable. Composite likelihoods, using lower dimensional components, and Stephenson-Tawn

更新日期：2020-07-27
• Extremes (IF 1.136) Pub Date : 2020-07-22
Wanfang Chen, Stefano Castruccio, Marc G. Genton

Saudi Arabia has been seeking to reduce its dependence on oil by diversifying its energy portfolio, including the largely underused energy potential from wind. However, extreme winds can possibly disrupt the wind turbine operations, thus preventing the stable and continuous production of wind energy. In this study, we assess the risk of disruptions of wind turbine operations, based on return levels

更新日期：2020-07-22
• Extremes (IF 1.136) Pub Date : 2020-07-14
Martin Bladt, Hansjörg Albrecher, Jan Beirlant

We consider removing lower order statistics from the classical Hill estimator in extreme value statistics, and compensating for it by rescaling the remaining terms. Trajectories of these trimmed statistics as a function of the extent of trimming turn out to be quite flat near the optimal threshold value. For the regularly varying case, the classical threshold selection problem in tail estimation is

更新日期：2020-07-14
• Extremes (IF 1.136) Pub Date : 2020-07-09
Malin Palö Forsström, Jeffrey E. Steif

We develop a formula for the power-law decay of various sets for symmetric stable random vectors in terms of how many vectors from the support of the corresponding spectral measure are needed to enter the set. One sees different decay rates in “different directions”, illustrating the phenomenon of hidden regular variation. We give several examples and obtain quite varied behavior, including sets which

更新日期：2020-07-09
• Extremes (IF 1.136) Pub Date : 2020-06-28
Bikramjit Das, Marie Kratz

Measures of risk concentration and their asymptotic behavior for portfolios with heavy-tailed risk factors is of interest in risk management. Second order regular variation is a structural assumption often imposed on such risk factors to study their convergence rates. In this paper, we provide the asymptotic rate of convergence of the measure of risk concentration for a portfolio of heavy-tailed risk

更新日期：2020-06-28
• Extremes (IF 1.136) Pub Date : 2020-06-26
Christian Rohrbeck, Emma S. Simpson, Ross P. Towe

This paper details the approach of team Lancaster to the 2019 EVA data challenge, dealing with spatio-temporal modelling of Red Sea surface temperature anomalies. We model the marginal distributions and dependence features separately; for the former, we use a combination of Gaussian and generalised Pareto distributions, while the dependence is captured using a localised Gaussian process approach. We

更新日期：2020-06-26
• Extremes (IF 1.136) Pub Date : 2020-06-16
Hideaki Kusumoto, Atsushi Takeuchi

Consider the maximum of independent and identically distributed random variables. The classical result says that the renormalized sample maximum converges to an extreme value distributions, under certain conditions on the distribution function. In the present paper, we shall study the uniform rate of the convergence with respect to the Kolmogorov distance in the framework of the Stein equations. Some

更新日期：2020-06-16
• Extremes (IF 1.136) Pub Date : 2020-06-09
Michael L. Stein

When making inferences about extreme quantiles, using simple parametric models for the entire distribution can be problematic in that a model that accurately describes the bulk of the distribution may lead to substantially biased estimates of extreme quantiles if the model is misspecified. One way to address this problem is to use flexible parametric families of distributions. For the setting where

更新日期：2020-06-09
• Extremes (IF 1.136) Pub Date : 2020-06-03
Axel Bücher, Jona Lilienthal, Paul Kinsvater, Roland Fried

A common statistical problem in hydrology is the estimation of annual maximal river flow distributions and their quantiles, with the objective of evaluating flood protection systems. Typically, record lengths are short and estimators imprecise, so that it is advisable to exploit additional sources of information. However, there is often uncertainty about the adequacy of such information, and a strict

更新日期：2020-06-03
• Extremes (IF 1.136) Pub Date : 2020-06-02

In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and alternatively also as the absorption time of a semi-Markov process with Mittag-Leffler distributed interarrival times. We then identify this class and its power transforms

更新日期：2020-06-02
• Extremes (IF 1.136) Pub Date : 2020-04-27
Milan Stehlík, Jozef Kiseľák, Marijus Vaičiulis, Pavlina Jordanova, Ludy Núñez Soza, Zdeněk Fabián, Philipp Hermann, Luboš Střelec, Andrés Rivera, Stéphane Girard, Sebastián Torres

We acknowledge the priority on the introduction of the formula of t-lgHill estimator for the positive extreme value index. We provide a novel motivation for this estimator based on ecologically driven dynamical systems. Another motivation is given directly by applying the general t-Hill procedure to log-gamma distribution. We illustrate the good quality of t-lgHill estimator in comparison to classical

更新日期：2020-04-27
• Extremes (IF 1.136) Pub Date : 2020-03-21
Natalia M. Markovich, Igor V. Rodionov

We study non-stationary random length sequences of random variables with regularly varying tails. Tail and extremal indexes of their maxima and linear combinations are found. We obtain conditions when both sums and maxima of these sequences have the same tail and extremal indexes. Their extremal index corresponds to the tail index of the most heavy-tailed random variable in the sequence.

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2020-03-05
Holger Drees, Miran Knežević

The extreme value dependence of regularly varying stationary time series can be described by the spectral tail process. Drees et al. (Extremes 18(3), 369–402, 2015) proposed estimators of the marginal distributions of this process based on exceedances over high deterministic thresholds and analyzed their asymptotic behavior. In practice, however, versions of the estimators are applied which use exceedances

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2020-03-02
Jan Holešovský, Michal Fusek

The extremal index is an important parameter in the characterization of extreme values of a stationary sequence, since it measures short-range dependence at extreme values, and governs clustering of extremes. This paper presents a novel approach to estimation of the extremal index based on artificial censoring of inter-exceedance times. The censored estimator based on the maximum likelihood method

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-08-30
Takuma Yoshida

This study investigates simultaneous confidence bands for extremal quantile regressions using the spline method. We construct the spline estimator for intermediate order quantiles using a conventional quantile regression framework, and we obtain the extreme order quantile estimator by extrapolating the spline estimator for intermediate order quantiles. We establish the asymptotic normality of the spline

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-12-13
Clemonell Bilayi-Biakana, Rafał Kulik, Philippe Soulier

We consider stationary time series $$\{X_{j},j\in \mathbb {Z}\}$$ whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each h ≥ 1, conditionally on X0 to exceed a threshold tending to infinity, the conditional distribution of Xh suitably normalized converges weakly to a non degenerate distribution. We consider in this paper the estimation of the

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-09-03
Aline Mefleh, Romain Biard, Clément Dombry, Zaher Khraibani

There are some suggestions that extreme weather events are becoming more frequent due to global warming. From a statistical point of view, this raises the question of trend detection in the extremes of a series of observations. We build upon the heteroscedastic extremes framework by Einmahl et al. (J. R. Stat. Soc. Ser. B. Stat. Methodol. 78(1), 31–51, 2016) where the observations are assumed independent

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-08-09
Phyllis Wan, Tiandong Wang, Richard A. Davis, Sidney I. Resnick

Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However, there are often difficulties fitting parametric network models to data due to either model error or data corruption. In this paper, we consider semi-parametric estimation

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-08-14
Jan-Frederik Mai

The set $$\mathfrak {L}$$ of infinite-dimensional, symmetric stable tail dependence functions associated with exchangeable max-stable sequences of random variables with unit Fréchet margins is shown to be a simplex. Except for a single element, the extremal boundary of $$\mathfrak {L}$$ is in one-to-one correspondence with the set $$\mathfrak {F}_{1}$$ of distribution functions of non-negative random

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-09-11
Dmitry Korshunov, Longmin Wang

Let X(t), $$t\in \mathbb {R}$$, be a d-dimensional vector-valued Brownian motion, d ≥ 1. For all $$\boldsymbol {b}\in \mathbb {R}^{d}\setminus (-\infty ,0]^{d}$$ we derive exact asymptotics of $$\mathbb{P}\{\boldsymbol{X}(t+s)-\boldsymbol{X}(t) >u\boldsymbol{b}\text{ for some } t\in[0,T],\ s\in[0,1]\} \quad\text{as } u\to\infty,$$ that is the asymptotical behavior of tail distribution of vector-valued

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-09-05
Sojung Kim, Kyoung-Kuk Kim, Heelang Ryu

In risk quantification of extreme events in multiple dimensions, a correct specification of the dependence structure among variables is difficult due to the limited size of effective data. This paper studies the problem of estimating quantiles for bivariate extreme value distributions, considering that an estimated Pickands dependence function may deviate from the truth within some fixed distance.

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2020-02-26
Christian Y. Robert

We consider the class of simple Brown-Resnick max-stable processes whose spectral processes are continuous exponential martingales. We develop the asymptotic theory for the realized power variations of these max-stable processes, that is, sums of powers of absolute increments. We consider an infill asymptotic setting, where the sampling frequency converges to zero while the time span remains fixed

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2020-02-18

Among bivariate tail dependence measures, the tail dependence coefficient has emerged as the popular choice. Akin to the correlation matrix, a multivariate dependence measure is constructed using these bivariate measures, and this is referred to in the literature as the tail dependence matrix (TDM). While the problem of determining whether a given d × d matrix is a correlation matrix is of the order

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2020-02-05
Gordon V. Chavez

We present a stochastic volatility modeling method that enables flexible and computationally efficient estimation of time-varying extreme event probabilities in heavy-tailed and nonlinearly dependent time series. Our approach uses a white noise process with conditionally log-Laplace volatility. In contrast to other, similar stochastic volatility frameworks, this process has analytic expressions for

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2020-01-22
Jose Blanchet, Fei He, Karthyek Murthy

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 the standard Extremal Types Theorem. Typical studies in distributional robustness involve computing worst case estimates over a model uncertainty region expressed

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2020-01-16
Raphaël Huser

Large, non-stationary spatio-temporal data are ubiquitous in modern statistical applications, and the modeling of spatio-temporal extremes is crucial for assessing risks in environmental sciences among others. While the modeling of extremes is challenging in itself, the prediction of rare events at unobserved spatial locations and time points is even more difficult. In this Editorial, we describe the

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2020-01-14
Clément Albert, Anne Dutfoy, Stéphane Girard

We investigate the asymptotic behavior of the (relative) extrapolation error associated with some estimators of extreme quantiles based on extreme-value theory. It is shown that the extrapolation error can be interpreted as the remainder of a first order Taylor expansion. Necessary and sufficient conditions are then provided such that this error tends to zero as the sample size increases. Interestingly

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-12-16
Boris Beranger, Simone A. Padoan, Scott A. Sisson

Estimation of extreme quantile regions, spaces in which future extreme events can occur with a given low probability, even beyond the range of the observed data, is an important task in the analysis of extremes. Existing methods to estimate such regions are available, but do not provide any measures of estimation uncertainty. We develop univariate and bivariate schemes for estimating extreme quantile

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-07-22
Nicolas Chenavier, Werner Nagel

A planar stationary and isotropic STIT tessellation at time t > 0 is observed in the window $$W_{\rho }={t^{-1}}\sqrt {\pi \ \rho }\cdot [-\frac {1}{2},\frac {1}{2}]^{2}$$, for ρ > 0. With each cell of the tessellation, we associate the inradius, which is the radius of the largest disk contained in the cell. Using the Chen-Stein method, we compute the limit distributions of the largest order statistics

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-05-28
Gilles Stupfler

Motivated by theoretical similarities between the classical Hill estimator of the tail index of a heavy-tailed distribution and one of its pseudo-estimator versions featuring a non-random threshold, we show a novel asymptotic representation of a class of empirical average excesses above a high random threshold, expressed in terms of order statistics, using their counterparts based on a suitable non-random

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-06-22
Julien Worms, Rym Worms

The Weibull-tail class of distributions is a sub-class of the Gumbel extreme domain of attraction, and it has caught the attention of a number of researchers in the last decade, particularly concerning the estimation of the so-called Weibull-tail coefficient. In this paper, we propose an estimator of this Weibull-tail coefficient when the Weibull-tail distribution of interest is censored from the right

更新日期：2020-04-21
• Extremes (IF 1.136) Pub Date : 2019-08-01
Hanan Ahmed, John H. J. Einmahl

Abstract 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 consider the situation where we have next to the n observations of interest another n + m observations of one or more related variables, like, e.g., financial

更新日期：2020-03-20
• Extremes (IF 1.136) Pub Date : 2019-06-20
Tom Stindl, Feng Chen

Abstract Extreme return financial time series are often challenging to model due to the presence of heavy temporal clustering of extremes and strong bursts of return volatility. One approach to model both these phenomena in extreme financial returns is the marked Hawkes self-exciting process. However, the Hawkes process restricts the arrival times of exogenously driven returns to follow a Poisson process

更新日期：2020-03-20
• Extremes (IF 1.136) Pub Date : 2015-10-20
Dan Cheng,Armin Schwartzman

Let {f(t) : t ∈ T} be a smooth Gaussian random field over a parameter space T, where T may be a subset of Euclidean space or, more generally, a Riemannian manifold. We provide a general formula for the distribution of the height of a local maximum [Formula: see text] is a local maximum of f(t)} when f is non-stationary. Moreover, we establish asymptotic approximations for the overshoot distribution

更新日期：2019-11-01
• Extremes (IF 1.136) Pub Date : 2014-01-21
Mark M Meerschaert,Hans-Peter Scheffler,Stilian A Stoev

A new approach to extreme value theory is presented for vector data with heavy tails. The tail index is allowed to vary with direction, where the directions are not necessarily along the coordinate axes. Basic asymptotic theory is developed, using operator regular variation and extremal integrals. A test is proposed to judge whether the tail index varies with direction in any given data set.

更新日期：2019-11-01
• Extremes (IF 1.136) Pub Date : 2013-09-24
Montserrat Fuentes,John Henry,Brian Reich

Estimating the probability of extreme temperature events is difficult because of limited records across time and the need to extrapolate the distributions of these events, as opposed to just the mean, to locations where observations are not available. Another related issue is the need to characterize the uncertainty in the estimated probability of extreme events at different locations. Although the

更新日期：2019-11-01
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