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  • Estimation of extremes for Weibull-tail distributions in the presence of random censoring
    Extremes (IF 1.778) Pub Date : 2019-06-22
    Julien Worms, Rym Worms

    Abstract 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

    更新日期:2020-03-24
  • Maxima and sums of non-stationary random length sequences
    Extremes (IF 1.778) Pub Date : 2020-03-21
    Natalia M. Markovich, Igor V. Rodionov

    Abstract 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:2020-03-22
  • Peak-over-threshold estimators for spectral tail processes: random vs deterministic thresholds
    Extremes (IF 1.778) Pub Date : 2020-03-05
    Holger Drees, Miran Knežević

    Abstract 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

    更新日期:2020-03-20
  • Estimation of the extremal index using censored distributions
    Extremes (IF 1.778) Pub Date : 2020-03-02
    Jan Holešovský, Michal Fusek

    Abstract 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

    更新日期:2020-03-20
  • Simultaneous confidence bands for extremal quantile regression with splines
    Extremes (IF 1.778) Pub Date : 2019-08-30
    Takuma Yoshida

    Abstract 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

    更新日期:2020-03-20
  • Statistical inference for heavy tailed series with extremal independence
    Extremes (IF 1.778) Pub Date : 2019-12-13
    Clemonell Bilayi-Biakana, Rafał Kulik, Philippe Soulier

    Abstract 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

    更新日期:2020-03-20
  • Trend detection for heteroscedastic extremes
    Extremes (IF 1.778) Pub Date : 2019-09-03
    Aline Mefleh, Romain Biard, Clément Dombry, Zaher Khraibani

    Abstract 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

    更新日期:2020-03-20
  • Are extreme value estimation methods useful for network data?
    Extremes (IF 1.778) Pub Date : 2019-08-09
    Phyllis Wan, Tiandong Wang, Richard A. Davis, Sidney I. Resnick

    Abstract 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

    更新日期:2020-03-20
  • Canonical spectral representation for exchangeable max-stable sequences
    Extremes (IF 1.778) Pub Date : 2019-08-14
    Jan-Frederik Mai

    Abstract 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

    更新日期:2020-03-20
  • Tail asymptotics for Shepp-statistics of Brownian motion in ℝd$\mathbb {R}^{d}$
    Extremes (IF 1.778) Pub Date : 2019-09-11
    Dmitry Korshunov, Longmin Wang

    Abstract 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

    更新日期:2020-03-20
  • Robust quantile estimation under bivariate extreme value models
    Extremes (IF 1.778) Pub Date : 2019-09-05
    Sojung Kim, Kyoung-Kuk Kim, Heelang Ryu

    Abstract 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:2020-03-20
  • Power variations for a class of Brown-Resnick processes
    Extremes (IF 1.778) Pub Date : 2020-02-26
    Christian Y. Robert

    Abstract 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

    更新日期:2020-03-20
  • On tail dependence matrices
    Extremes (IF 1.778) Pub Date : 2020-02-18
    Nariankadu D. Shyamalkumar, Siyang Tao

    Abstract 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

    更新日期:2020-03-20
  • Dynamic tail inference with log-Laplace volatility
    Extremes (IF 1.778) Pub Date : 2020-02-05
    Gordon V. Chavez

    Abstract 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

    更新日期:2020-03-20
  • On distributionally robust extreme value analysis
    Extremes (IF 1.778) Pub Date : 2020-01-22
    Jose Blanchet, Fei He, Karthyek Murthy

    Abstract 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

    更新日期:2020-03-20
  • Editorial: EVA 2019 data competition on spatio-temporal prediction of Red Sea surface temperature extremes
    Extremes (IF 1.778) Pub Date : 2020-01-16
    Raphaël Huser

    Abstract 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

    更新日期:2020-03-20
  • Asymptotic behavior of the extrapolation error associated with the estimation of extreme quantiles
    Extremes (IF 1.778) Pub Date : 2020-01-14
    Clément Albert, Anne Dutfoy, Stéphane Girard

    Abstract 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.

    更新日期:2020-03-20
  • Estimation and uncertainty quantification for extreme quantile regions
    Extremes (IF 1.778) Pub Date : 2019-12-16
    Boris Beranger, Simone A. Padoan, Scott A. Sisson

    Abstract 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

    更新日期:2020-03-20
  • Improved estimation of the extreme value index using related variables
    Extremes (IF 1.778) 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
  • The largest order statistics for the inradius in an isotropic STIT tessellation
    Extremes (IF 1.778) Pub Date : 2019-07-22
    Nicolas Chenavier, Werner Nagel

    Abstract 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

    更新日期:2020-03-20
  • On a relationship between randomly and non-randomly thresholded empirical average excesses for heavy tails
    Extremes (IF 1.778) Pub Date : 2019-05-28
    Gilles Stupfler

    Abstract 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

    更新日期:2020-03-20
  • Modeling extreme negative returns using marked renewal Hawkes processes
    Extremes (IF 1.778) 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
  • Distribution of the Height of Local Maxima of Gaussian Random Fields.
    Extremes (IF 1.778) 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
  • EXTREME VALUE THEORY WITH OPERATOR NORMING.
    Extremes (IF 1.778) 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
  • Nonparametric Spatial Models for Extremes: Application to Extreme Temperature Data.
    Extremes (IF 1.778) 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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