A weighted mean excess function approach to the estimation of Weibull-type tails

Goegebeur, Yuri; Guillou, Armelle

doi:10.1007/s11749-010-0190-6

Cited by 5 publications

(6 citation statements)

References 20 publications

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“…Similar conditions can be found in Gardes & Girard (2008a) and Goegebeur & Guillou (2011) in the framework of the estimation of Weibull‐type tails. We also refer to Mason (1981) for general results on asymptotic normality for linear combinations of order statistics.…”

Section: A Functional Estimator For ηsupporting

confidence: 69%

Asymptotically Unbiased Estimation of the Coefficient of Tail Dependence

Goegebeur

Guillou

2012

Scandinavian J Statistics

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We introduce and study a class of weighted functional estimators for the coefficient of tail dependence in bivariate extreme value statistics. Asymptotic normality of these estimators is established under a second order condition on the joint tail behavior, some conditions on the weight function and for appropriately chosen sequences of intermediate order statistics.Asymptotically unbiased estimators are constructed by judiciously chosen linear combinations of weighted functional estimators, and variance optimality within this class of asymptotically unbiased estimators is discussed. The finite sample performance of some specific examples from our class of estimators and some alternatives from the recent literature are evaluated with a small simulation experiment.

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Section: A Functional Estimator For ηsupporting

confidence: 69%

Asymptotically Unbiased Estimation of the Coefficient of Tail Dependence

Goegebeur

Guillou

2012

Scandinavian J Statistics

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“…Assumption (R) is well accepted in the literature. It was formulated in a slightly different form in Diebolt et al (2008) and Goegebeur and Guillou (2011) in the Weibull-type framework, and Gardes and Girard (2008b) invoked it for tail analysis in the Fréchet max-domain of attraction.…”

Section: Construction and Asymptotic Propertiesmentioning

confidence: 99%

“…The figure indicates that the estimates for the tail coefficient generally follow the pattern in the data in that the estimates tend to be larger at SW L positions where the extreme Hm O measurements show larger spacings. To illustrate the extra flexibility of our approach, we also performed a univariate analysis of the tail of the Hm O distribution, thus ignoring the information in SW L, using the mean excess-based estimator for θ proposed in Goegebeur and Guillou (2011). Figure 1d shows these univariate estimates for the Weibull-tail coefficient of the variable Hm O as a function of k. This plot suggests a stable estimate of θ for k values between 50 and 100, with median 0.42.…”

Section: Case Study: Sea Storm Datamentioning

confidence: 99%

“…In the analysis of univariate Weibull-type tails, the estimation of θ and the subsequent estimation of upper extreme quantiles assume a central position. We refer to Broniatowski (1993), Beirlant et al (1995), Girard (2004), Girard (2005, 2008a), Diebolt et al (2008), Dierckx et al (2009), , Goegebeur and Guillou (2011), and the references therein.…”

Section: Introductionmentioning

confidence: 99%

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Kernel regression with Weibull-type tails

et al. 2015

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International audienceWe consider the estimation of the tail coefficient of a Weibull-type distribution in the presence of random covariates. The approach followed is non-parametric and consists of locally weighted estimation in narrow neighbourhoods in the covariate space. We introduce two families of estimators and study their asymptotic behaviour under some conditions on the conditional response distribution, the kernel function, the density function of the independent variables, and for appropriately chosen bandwidth and threshold parameters. We also introduce a Weissman-type estimator for estimating upper extreme conditional quantiles. The finite sample behaviour of the proposed estimators is examined with a simulation experiment. The practical applicability of the methodology is illustrated on a dataset of sea storm measurements

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“…There is an extensive literature on the analysis of univariate Weibulltype tails, such as Berred (1991), Broniatowski (1993), Girard (2004), Girard, 2005, 2008), Diebolt et al (2008), Goegebeur et al (2010) and Goegebeur and Guillou (2011). In contrast, there are only few studies on investigating the extremal behavior of Weibull-type tails under the regression setting.…”

Section: Introductionmentioning

confidence: 99%

Extremal linear quantile regression with Weibull-type tails

Wang

Tong³

2020

STAT SINICA

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This paper studies the estimation of extreme conditional quantiles for distributions with Weibull-type tails. We propose two families of estimators for the Weibull tail-coefficient, and construct an extrapolation estimator for the extreme conditional quantiles based on quantile regression and extreme value theory. The asymptotic results of the proposed estimators are established. The work fills a gap in the literature of extreme quantile regression where many important Weibull-type distributions are excluded by the assumed strong conditions. We demonstrate through simulation study that the proposed Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing) Extremal linear quantile regression with Weibull-type tails extrapolation method provides more efficient and stable estimation of conditional quantiles of extreme orders than the conventional method.The practical value of the proposed method is demonstrated through the analysis of extremely high birth weight.

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A weighted mean excess function approach to the estimation of Weibull-type tails

Abstract: Weibull-type distribution, Weibull-tail coefficient, Mean excess function, Bias reduction, 62G05, 62G20, 62G30, 62G32,

Cited by 5 publications

References 20 publications

Asymptotically Unbiased Estimation of the Coefficient of Tail Dependence

Asymptotically Unbiased Estimation of the Coefficient of Tail Dependence

Kernel regression with Weibull-type tails

Extremal linear quantile regression with Weibull-type tails

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