A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Guillotte, Simon; Perron, FranÃ§ois

doi:10.1002/cjs.5550360304

Cited by 13 publications

(11 citation statements)

References 20 publications

(27 reference statements)

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“…Some examples focused on nonparametric estimators of the Pickands dependence function (Pickands 1981) are provided in Capéraà et al (1997), Genest and Segers (2009), Bücher et al (2011), Berghaus et al (2013) and Marcon et al (2015), among others. Examples of Bayesian modelling of the extremal dependence are Boldi and Davison (2007), Guillotte and Perron (2008) and Sabourin and Naveau (2014) to cite a few.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference for the extremal dependence

Marcon¹,

Padoan²,

Antoniano-Villalobos³

2016

Electron. J. Statist.

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A simple approach for modeling multivariate extremes is to consider the vector of component-wise maxima and their max-stable distributions. The extremal dependence can be inferred by estimating the angular measure or, alternatively, the Pickands dependence function. We propose a nonparametric Bayesian model that allows, in the bivariate case, the simultaneous estimation of both functional representations through the use of polynomials in the Bernstein form. The constraints required to provide a valid extremal dependence are addressed in a straightforward manner, by placing a prior on the coefficients of the Bernstein polynomials which gives probability one to the set of valid functions. The prior is extended to the polynomial degree, making our approach fully nonparametric. Although the analytical expression of the posterior is unknown, inference is possible via a trans-dimensional MCMC scheme. We show the efficiency of the proposed methodology by means of a simulation study. The extremal behaviour of log-returns of daily exchange rates between the Pound Sterling vs the U.S. Dollar and the Pound Sterling vs the Japanese Yen is analysed for illustrative purposes.MSC 2010 subject classifications: 62G05, 62G07, 62G32.

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Section: Introductionmentioning

confidence: 99%

Bayesian inference for the extremal dependence

Marcon¹,

Padoan²,

Antoniano-Villalobos³

2016

Electron. J. Statist.

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“…Finally, a nonparametric Bayesian approach has been proposed by Guillotte and Perron [43]. Driven by a nonparametric likelihood, their methodology yields an estimator with good properties: its estimation error is typically small, it automatically verifies the shape constraints, and it blends naturally with parametric likelihood methods for the margins.…”

Section: Nonparametric Estimationmentioning

confidence: 99%

Extreme-Value Copulas

Gudendorf

Segers

2010

Lecture Notes in Statistics

174

138

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Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise naturally in the domain of extreme-value theory, they can also be a convenient choice to model general positive dependence structures. The aim of this survey is to present the reader with the state-of-the-art in dependence modeling via extreme-value copulas. Both probabilistic and statistical issues are reviewed, in a nonparametric as well as a parametric context.

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“…As in Zhang et al (2008), the setting here is that of a random sample from a distribution whose margins are known and whose copula is an extreme-value copula. It would be worthwhile to extend this to the case of unknown margins (Guillotte and Perron, 2008;Genest and Segers, 2009) and the case that the copula of F is merely in the domain of attraction of an extreme-value copula (Capéraà and Fougères, 2000;Einmahl and Segers, 2009).…”

Section: Introductionmentioning

confidence: 99%

Nonparametric estimation of an extreme-value copula in arbitrary dimensions

Gudendorf

Segers

2011

Journal of Multivariate Analysis

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a b s t r a c tInference on an extreme-value copula usually proceeds via its Pickands dependence function, which is a convex function on the unit simplex satisfying certain inequality constraints. In the setting of an i.i.d. random sample from a multivariate distribution with known margins and an unknown extreme-value copula, an extension of the Capéraà-Fougères-Genest estimator was introduced by D. Zhang, M. T. Wells and L. Peng [Nonparametric estimation of the dependence function for a multivariate extreme-value distribution, Journal of Multivariate Analysis 99 (4) (2008) 577-588]. The joint asymptotic distribution of the estimator as a random function on the simplex was not provided. Moreover, implementation of the estimator requires the choice of a number of weight functions on the simplex, the issue of their optimal selection being left unresolved.A new, simplified representation of the CFG-estimator combined with standard empirical process theory provides the means to uncover its asymptotic distribution in the space of continuous, real-valued functions on the simplex. Moreover, the ordinary leastsquares estimator of the intercept in a certain linear regression model provides an adaptive version of the CFG-estimator whose asymptotic behavior is the same as if the varianceminimizing weight functions were used. As illustrated in a simulation study, the gain in efficiency can be quite sizable.

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A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Cited by 13 publications

References 20 publications

Bayesian inference for the extremal dependence

Bayesian inference for the extremal dependence

Extreme-Value Copulas

Nonparametric estimation of an extreme-value copula in arbitrary dimensions

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