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  • A regionalisation approach for rainfall based on extremal dependence
    Extremes (IF 1.136) Pub Date : 2020-10-07
    K. R. Saunders, A. G. Stephenson, D. J. Karoly

    To mitigate the risk posed by extreme rainfall events, we require statistical models that reliably capture extremes in continuous space with dependence. However, assuming a stationary dependence structure in such models is often erroneous, particularly over large geographical domains. Furthermore, there are limitations on the ability to fit existing models, such as max-stable processes, to a large

    更新日期:2020-10-07
  • Bayesian space-time gap filling for inference on extreme hot-spots: an application to Red Sea surface temperatures
    Extremes (IF 1.136) Pub Date : 2020-09-15
    Daniela Castro-Camilo, Linda Mhalla, Thomas Opitz

    We develop a method for probabilistic prediction of extreme value hot-spots in a spatio-temporal framework, tailored to big datasets containing important gaps. In this setting, direct calculation of summaries from data, such as the minimum over a space-time domain, is not possible. To obtain predictive distributions for such cluster summaries, we propose a two-step approach. We first model marginal

    更新日期:2020-09-15
  • Extreme value theory for anomaly detection – the GPD classifier
    Extremes (IF 1.136) Pub Date : 2020-09-09
    Edoardo Vignotto, Sebastian Engelke

    Classification tasks usually assume that all possible classes are present during the training phase. This is restrictive if the algorithm is used over a long time and possibly encounters samples from unknown new classes. It is therefore fundamental to develop algorithms able to distinguish between normal and abnormal test data. In the last few years, extreme value theory has become an important tool

    更新日期:2020-09-10
  • Ordinal patterns in clusters of subsequent extremes of regularly varying time series
    Extremes (IF 1.136) Pub Date : 2020-08-24
    Marco Oesting, Alexander Schnurr

    In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and the ordinal patterns giving the relative positions of the data points within a cluster. Since these patterns take only the ordinal structure of consecutive data

    更新日期:2020-08-24
  • Extreme values of linear processes with heavy-tailed innovations and missing observations
    Extremes (IF 1.136) Pub Date : 2020-08-23
    Lenka Glavaš, Pavle Mladenović

    We investigate maxima in incomplete samples from strictly stationary random sequences defined as linear models of i.i.d. random variables with heavy-tailed innovations that satisfy the tail balance condition. Using the point process approach we obtain limit theorems for the sequence of random vectors whose components are properly normalized maxima in complete and incomplete samples.

    更新日期:2020-08-23
  • Basin-wide spatial conditional extremes for severe ocean storms
    Extremes (IF 1.136) Pub Date : 2020-08-21
    Rob Shooter, Jonathan Tawn, Emma Ross, Philip Jonathan

    Physical considerations and previous studies suggest that extremal dependence between ocean storm severity at two locations exhibits near asymptotic dependence at short inter-location distances, leading to asymptotic independence and perfect independence with increasing distance. We present a spatial conditional extremes (SCE) model for storm severity, characterising extremal spatial dependence of

    更新日期:2020-08-21
  • Exact asymptotics of component-wise extrema of two-dimensional Brownian motion
    Extremes (IF 1.136) Pub Date : 2020-08-11
    Krzysztof Dȩbicki, Lanpeng Ji, Tomasz Rolski

    We derive the exact asymptotics of $ {\mathbb {P} \left \{ \underset {t\ge 0}{\sup } \left (X_{1}(t) - \mu _{1} t\right )> u, \ \underset {s\ge 0}{\sup } \left (X_{2}(s) - \mu _{2} s\right )> u \right \} },\ \ u\to \infty , $ where (X1(t), X2(s))t, s≥ 0 is a correlated two-dimensional Brownian motion with correlation ρ ∈ [− 1,1] and μ1, μ2 > 0. It appears that the play between ρ and μ1, μ2 leads to

    更新日期:2020-08-12
  • Limit distributions of the upper order statistics for the Lévy-frailty Marshall-Olkin distribution
    Extremes (IF 1.136) Pub Date : 2020-08-07
    Javiera Barrera, Guido Lagos

    The Marshall-Olkin (MO) distribution is considered a key model in reliability theory and in risk analysis, where it is used to model the lifetimes of dependent components or entities of a system and dependency is induced by “shocks” that hit one or more components at a time. Of particular interest is the Lévy-frailty subfamily of the Marshall-Olkin (LFMO) distribution, since it has few parameters and

    更新日期:2020-08-08
  • High-dimensional inference using the extremal skew- t process
    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
  • Assessing the risk of disruption of wind turbine operations in Saudi Arabia using Bayesian spatial extremes
    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
  • Threshold selection and trimming in extremes
    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
  • A formula for hidden regular variation behavior for symmetric stable distributions
    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
  • Matrix Mittag–Leffler distributions and modeling heavy-tailed risks
    Extremes (IF 1.136) Pub Date : 2020-07-03
    Hansjörg Albrecher; Martin Bladt; Mogens Bladt

    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:2020-07-03
  • Risk concentration under second order regular variation
    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
  • A spatio-temporal model for Red Sea surface temperature anomalies
    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
  • Remark on rates of convergence to extreme value distributions via the Stein equations
    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
  • Parametric models for distributions when interest is in extremes with an application to daily temperature
    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
  • Penalized quasi-maximum likelihood estimation for extreme value models with application to flood frequency analysis
    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
  • Priority statement and some properties of t-lgHill estimator
    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
  • Editorial: EVA 2019 data competition on spatio-temporal prediction of Red Sea surface temperature extremes
    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
  • Estimation and uncertainty quantification for extreme quantile regions
    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
  • Maxima and sums of non-stationary random length sequences
    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:2020-03-21
  • Peak-over-threshold estimators for spectral tail processes: random vs deterministic thresholds
    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:2020-03-05
  • Estimation of the extremal index using censored distributions
    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:2020-03-02
  • Power variations for a class of Brown-Resnick processes
    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:2020-02-26
  • On tail dependence matrices
    Extremes (IF 1.136) Pub Date : 2020-02-18
    Nariankadu D. Shyamalkumar; Siyang Tao

    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:2020-02-18
  • Dynamic tail inference with log-Laplace volatility
    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:2020-02-05
  • On distributionally robust extreme value analysis
    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:2020-01-22
  • Asymptotic behavior of the extrapolation error associated with the estimation of extreme quantiles
    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:2020-01-14
  • Statistical inference for heavy tailed series with extremal independence
    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:2019-12-13
  • Tail asymptotics for Shepp-statistics of Brownian motion in ℝd$\mathbb {R}^{d}$
    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:2019-09-11
  • Robust quantile estimation under bivariate extreme value models
    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:2019-09-05
  • Trend detection for heteroscedastic extremes
    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:2019-09-03
  • Simultaneous confidence bands for extremal quantile regression with splines
    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:2019-08-30
  • Canonical spectral representation for exchangeable max-stable sequences
    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:2019-08-14
  • Are extreme value estimation methods useful for network data?
    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:2019-08-09
  • Improved estimation of the extreme value index using related variables
    Extremes (IF 1.136) Pub Date : 2019-08-01
    Hanan Ahmed; John H. J. Einmahl

    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 losses

    更新日期:2019-08-01
  • The largest order statistics for the inradius in an isotropic STIT tessellation
    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:2019-07-22
  • Improving precipitation forecasts using extreme quantile regression
    Extremes (IF 1.136) Pub Date : 2019-07-16
    Jasper Velthoen; Juan-Juan Cai; Geurt Jongbloed; Maurice Schmeits

    Aiming to estimate extreme precipitation forecast quantiles, we propose a nonparametric regression model that features a constant extreme value index. Using local linear quantile regression and an extrapolation technique from extreme value theory, we develop an estimator for conditional quantiles corresponding to extreme high probability levels. We establish uniform consistency and asymptotic normality

    更新日期:2019-07-16
  • Extremal dependence of random scale constructions
    Extremes (IF 1.136) Pub Date : 2019-07-12
    Sebastian Engelke; Thomas Opitz; Jennifer Wadsworth

    A bivariate random vector can exhibit either asymptotic independence or dependence between the largest values of its components. When used as a statistical model for risk assessment in fields such as finance, insurance or meteorology, it is crucial to understand which of the two asymptotic regimes occurs. Motivated by their ubiquity and flexibility, we consider the extremal dependence properties of

    更新日期:2019-07-12
  • Estimation of extremes for Weibull-tail distributions in the presence of random censoring
    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:2019-06-22
  • Modeling extreme negative returns using marked renewal Hawkes processes
    Extremes (IF 1.136) Pub Date : 2019-06-20
    Tom Stindl; Feng Chen

    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 and

    更新日期:2019-06-20
  • On the accuracy of Poisson approximation
    Extremes (IF 1.136) Pub Date : 2019-06-18
    S. Y. Novak

    The problem of evaluating the accuracy of Poisson approximation to the distribution of a sum of independent integer-valued random variables has attracted a lot of attention in the past six decades. From a practical point of view, it has important applications in insurance, reliability theory, extreme value theory, etc.; from a theoretical point of view, the topic provides insights into Kolmogorov’s

    更新日期:2019-06-18
  • On a relationship between randomly and non-randomly thresholded empirical average excesses for heavy tails
    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:2019-05-28
  • A nonparametric method for producing isolines of bivariate exceedance probabilities
    Extremes (IF 1.136) Pub Date : 2019-05-15
    Daniel Cooley; Emeric Thibaud; Federico Castillo; Michael F. Wehner

    We present a method for drawing isolines indicating regions of equal joint exceedance probability for bivariate data. The method relies on bivariate regular variation, a dependence framework widely used for extremes. The method we utilize for characterizing dependence in the tail is largely nonparametric. The extremes framework enables drawing isolines corresponding to very low exceedance probabilities

    更新日期:2019-05-15
  • On maximum of Gaussian random field having unique maximum point of its variance
    Extremes (IF 1.136) Pub Date : 2019-05-14
    Sergey G. Kobelkov; Vladimir I. Piterbarg

    Gaussian random fields on Euclidean spaces whose variances reach their maximum values at unique points are considered. Exact asymptotic behaviors of probabilities of large absolute maximum of theirs trajectories have been evaluated using Double Sum Method under the widest possible conditions.

    更新日期:2019-05-14
  • Extremes of stationary random fields on a lattice
    Extremes (IF 1.136) Pub Date : 2019-05-14
    Chengxiu Ling

    Extremal behavior of stationary Gaussian sequences/random fields is widely investigated since it models common cluster phenomena and brings a bridge between discrete and continuous extremes. We establish extensively limit theorems of stationary random fields under certain mixing and dependence conditions, which are further illustrated by typical examples of order statistics of Gaussian random fields

    更新日期:2019-05-14
  • The tail dependograph
    Extremes (IF 1.136) Pub Date : 2019-03-19
    Cécile Mercadier; Olivier Roustant

    All characterizations of non-degenerate multivariate tail dependence structures are both functional and infinite-dimensional. Taking advantage of the Hoeffding–Sobol decomposition, we derive new indices to measure and summarize the strength of dependence in a multivariate extreme value analysis. The tail superset importance coefficients provide a pairwise ordering of the asymptotic dependence structure

    更新日期:2019-03-19
  • Extremes of spherical fractional Brownian motion
    Extremes (IF 1.136) Pub Date : 2019-03-01
    Dan Cheng; Peng Liu

    Let \(\{B_{\beta } (x), x \in \mathbb {\mathbb S}^{N}\}\) be a fractional Brownian motion on the N-dimensional unit sphere \(\mathbb {S}^{N}\) with Hurst index β. We study the excursion probability \(\mathbb {P}\left \{{{\sup _{x\in T} B_{\beta }(x) > u }}\right \}\) and obtain the asymptotics as u →∞, where T can be the entire sphere \(\mathbb {S}^{N}\) or a geodesic disc on \(\mathbb {S}^{N}\).

    更新日期:2019-03-01
  • Bias-corrected estimation for conditional Pareto-type distributions with random right censoring
    Extremes (IF 1.136) Pub Date : 2019-02-07
    Yuri Goegebeur; Armelle Guillou; Jing Qin

    We consider bias-reduced estimation of the extreme value index in conditional Pareto-type models with random covariates when the response variable is subject to random right censoring. The bias-correction is obtained by fitting the extended Pareto distribution locally to the relative excesses over a high threshold using the maximum likelihood method. Convergence in probability and asymptotic normality

    更新日期:2019-02-07
  • The time of ultimate recovery in Gaussian risk model
    Extremes (IF 1.136) Pub Date : 2019-02-05
    Krzysztof Dȩbicki; Peng Liu

    We analyze the distance \(\mathcal {R}_{T}(u)\) between the first and the last passage time of {X(t) − ct : t ∈ [0, T]} at level u in time horizon T ∈ (0, ∞], where X is a centered Gaussian process with stationary increments and \(c\in {\mathbb {R}}\), given that the first passage time occurred before T. Under some tractable assumptions on X, we find Δ(u) and G(x) such that$$\lim\limits_{u\to\infty}\mathbb{P}

    更新日期:2019-02-05
  • Exceedance-based nonlinear regression of tail dependence
    Extremes (IF 1.136) Pub Date : 2019-01-30
    Linda Mhalla; Thomas Opitz; Valérie Chavez-Demoulin

    The probability and structure of co-occurrences of extreme values in multivariate data may critically depend on auxiliary information provided by covariates. In this contribution, we develop a flexible generalized additive modeling framework based on high threshold exceedances for estimating covariate-dependent joint tail characteristics for regimes of asymptotic dependence and asymptotic independence

    更新日期:2019-01-30
  • Identifying groups of variables with the potential of being large simultaneously
    Extremes (IF 1.136) Pub Date : 2019-01-05
    Maël Chiapino; Anne Sabourin; Johan Segers

    Identifying groups of variables that may be large simultaneously amounts to finding out which joint tail dependence coefficients of a multivariate distribution are positive. The asymptotic distribution of a vector of nonparametric, rank-based estimators of these coefficients justifies a stopping criterion in an algorithm that searches the collection of all possible groups of variables in a systematic

    更新日期:2019-01-05
  • Generalised least squares estimation of regularly varying space-time processes based on flexible observation schemes
    Extremes (IF 1.136) Pub Date : 2019-01-03
    Sven Buhl; Claudia Klüppelberg

    Regularly varying stochastic processes model extreme dependence between process values at different locations and/or time points. For such stationary processes we propose a two-step parameter estimation of the extremogram, when some part of the domain of interest is fixed and another increasing. We provide conditions for consistency and asymptotic normality of the empirical extremogram centred by a

    更新日期:2019-01-03
  • Ridge regression estimators for the extreme value index
    Extremes (IF 1.136) Pub Date : 2018-10-10
    Sven Buitendag; Jan Beirlant; Tertius de Wet

    We consider bias reduced estimators of the extreme value index (EVI) in case of Pareto-type distributions and under all max-domains of attraction. To this purpose we revisit the regression approach started in Feuerverger and Hall (Ann. Stat. 27, 760–781, 1999) and Beirlant et al. (Extremes 2, 177–200, 1999) in the case of a positive EVI, and in Beirlant et al. (2005) for real-valued EVI. We generalize

    更新日期:2018-10-10
  • Managing local dependencies in asymptotic theory for maxima of stationary random fields
    Extremes (IF 1.136) Pub Date : 2018-10-08
    Adam Jakubowski; Natalia Soja-Kukieła

    In the paper we solve the limit problem for partial maxima of m-dependent stationary random fields and we extend the obtained solution to fields satisfying some local mixing conditions. New methods for describing the limitting distribution of maxima are proposed. A notion of a phantom distribution function for a random field is investigated. As an application, several original formulas for calculation

    更新日期:2018-10-08
  • Multiple thresholds in extremal parameter estimation
    Extremes (IF 1.136) Pub Date : 2018-10-03
    Julian Sun; Gennady Samorodnitsky

    Selecting the number of upper order statistics to use in extremal inference or selecting the threshold above which we perform the extremal inference is a common step in applications of extreme value theory. Not only is the selection itself difficult, but the large part of the sample below the threshold may potentially carry useful information. We propose an approach that takes an extremal parameter

    更新日期:2018-10-03
  • Consistency of Hill estimators in a linear preferential attachment model
    Extremes (IF 1.136) Pub Date : 2018-09-08
    Tiandong Wang; Sidney I. Resnick

    Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. Statistical estimates of the tail exponent of the power-law degree distribution often use the Hill estimator as one of the key summary statistics. The consistency of the Hill estimator for network data has not been explored and the major goal in this paper is to prove

    更新日期:2018-09-08
  • Estimation of the expected shortfall given an extreme component under conditional extreme value model
    Extremes (IF 1.136) Pub Date : 2018-09-05
    Rafał Kulik; Zhigang Tong

    For two risks, X and Y, the Marginal Expected Shortfall (MES) is defined as \(\mathbb {E}[Y\mid X>F_{X}^{\leftarrow }(1-p)]\), where FX is the distribution function of X and p is small. In this paper we establish consistency and asymptotic normality of an estimator of MES on assuming that (X, Y ) follows a Conditional Extreme Value (CEV) model. The theoretical findings are supported by simulation studies

    更新日期:2018-09-05
  • Discussion of “human life is unlimited-but short” by H Rootzén and D Zholud
    Extremes (IF 1.136) Pub Date : 2018-08-14
    Olle Nerman

    The statistical paper human life is short-but unlimited is briefly discussed. The possibilities and limitations of statistical inference concerning very long human life spans are considered. The restricted models of tail distributions that arise from assumption of renormalized convergence of max- or conditional peaks over thresholds-distributions are questioned in the application context of the reviewed

    更新日期:2018-08-14
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