Non-Parametric Bayesian Inference on Bivariate Extremes

Guillotte, Simon; Perron, François; Segers, Johan

doi:10.1111/j.1467-9868.2010.00770.x

Cited by 35 publications

(25 citation statements)

References 55 publications

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“…Segers (2009) andde Carvalho & use empirical likelihood to impose the mean constraint (Equation 14) when estimating bivariate extreme-value distributions, and this seems a promising approach that can be broadly applied. Semiparametric models that satisfy the mean constraints have been proposed and fitted using Markov chain Monte Carlo algorithms by Boldi & Davison (2007), Guillotte et al (2011), andSabourin &Naveau (2014).…”

Section: More Complex Settingsmentioning

confidence: 99%

Statistics of Extremes

Davison

Huser

2015

Annu. Rev. Stat. Appl.

166

126

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Statistics of extremes concerns inference for rare events. Often the events have never yet been observed, and their probabilities must therefore be estimated by extrapolation of tail models fitted to available data. Because data concerning the event of interest may be very limited, efficient methods of inference play an important role. This article reviews this domain, emphasizing current research topics. We first sketch the classical theory of extremes for maxima and threshold exceedances of stationary series. We then review multivariate theory, distinguishing asymptotic independence and dependence models, followed by a description of models for spatial and spatiotemporal extreme events. Finally, we discuss inference and describe two applications. Animations illustrate some of the main ideas. 9.1

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Section: More Complex Settingsmentioning

confidence: 99%

Statistics of Extremes

Davison

Huser

2015

Annu. Rev. Stat. Appl.

166

126

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“…Under a standard assumption of multivariate regular variation (see Section 2), the distribution of excesses above large thresholds is characterized by parametric marginal distributions and a non-parametric dependence structure that is independent from threshold. Since the family of admissible dependence structures is, by nature, too large to be fully described by any parametric model, non-parametric estimation has received a great deal of attention in the past few years (Einmahl et al, 2001;Einmahl and Segers, 2009;Guillotte et al, 2011). To the best of my knowledge, the non parametric estimators of the so-called angular measure (which characterizes the dependence structure among extremes) are only defined with exact data and their adaptation to censored data is far from straightforward.…”

Section: Introductionmentioning

confidence: 99%

Semi-parametric modeling of excesses above high multivariate thresholds with censored data

Sabourin

2015

Journal of Multivariate Analysis

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Please cite this article as: A. Sabourin, Semi-parametric modeling of excesses above high multivariate thresholds with censored data, Journal of Multivariate Analysis (2015), http://dx. AbstractHow to include censored data in a statistical analysis is a recurrent issue in statistics. In multivariate extremes, the dependence structure of large observations can be characterized in terms of a non parametric angular measure, while marginal excesses above asymptotically large thresholds have a parametric distribution. In this work, a flexible semi-parametric Dirichlet mixture model for angular measures is adapted to the context of censored data and missing components. One major issue is to take into account censoring intervals overlapping the extremal threshold, without knowing whether the corresponding hidden data is actually extreme. Further, the censored likelihood needed for Bayesian inference has no analytic expression. The first issue is tackled using a Poisson process model for extremes, whereas a data augmentation scheme avoids multivariate integration of the Poisson process intensity over both the censored intervals and the failure region above threshold. The implemented MCMC algorithm allows simultaneous estimation of marginal and dependence parameters, so that all sources of uncertainty other than model bias are captured by posterior credible intervals. The method is illustrated on simulated and real data.

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“…Einmahl and Segers (2009) propose an enhancement of the empirical spectral measure in Einmahl et al (2001) by enforcing the moment constraints with empirical likelihood methods. A nonparametric Bayesian method based on the censored-likelihood approach in Ledford and Tawn (1996) is proposed in Guillotte et al (2011).…”

Section: Introductionmentioning

confidence: 99%

A Euclidean Likelihood Estimator for Bivariate Tail Dependence

Carvalho

Oumow

Segers

et al. 2013

Communications in Statistics - Theory and Methods

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The spectral measure plays a key role in the statistical modeling of multivariate extremes.Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for the spectral measure which is simple and explicitly defined, with its expression being free of Lagrange multipliers. Our Numerical experiments suggest an overall good performance and identical behavior to the maximum empirical likelihood estimator. We illustrate the method in an extreme temperature data analysis.

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Non-Parametric Bayesian Inference on Bivariate Extremes

Cited by 35 publications

References 55 publications

Statistics of Extremes

Statistics of Extremes

Semi-parametric modeling of excesses above high multivariate thresholds with censored data

A Euclidean Likelihood Estimator for Bivariate Tail Dependence

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