Modelling Extreme Multivariate Events

Coles, Stuart; Tawn, Jonathan A.

doi:10.1111/j.2517-6161.1991.tb01830.x

Cited by 395 publications

(375 citation statements)

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“…This approach would require the specification of multivariate extreme distributions that may or may not take into account spatial dependence (see Pickands 1981;Coles and Tawn 1991;Rootzen and Tajvidi 2006;Padoan et al 2010).…”

Section: Final Remarksmentioning

confidence: 99%

Regression models for exceedance data via the full likelihood

2010

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Many situations in practice require appropriate specification of operating characteristics under extreme conditions. Typical examples include environmental sciences where studies include extreme temperature, rainfall and river flow to name a few. In these cases, the effect of geographic and climatological inputs are likely to play a relevant role. This paper is concerned with the study of extreme data in the presence of relevant auxiliary information. The underlying model involves a mixture distribution: a generalized Pareto distribution is assumed for the exceedances beyond a high threshold and a non-parametric approach is assumed for the data below the threshold. Thus, the full likelihood including data below and above the threshold is considered in the estimation. The main novelty is the introduction of a regression structure to explain the variation of the exceedances through all tail parameters. Estimation is performed under the Bayesian paradigm and includes model choice. This allows for determination of higher quantiles under each covariate configuration and upper bounds for the data, where appropriate. Simulation results show that the models are appropriate and identifiable. The models are applied to the study of two temperature F. F. do Nascimento (B) 123 496 Environ Ecol Stat (2011) 18:495-512 datasets: maxima in the U.S.A. and minima in Brazil, and compared to other related models.

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Section: Final Remarksmentioning

confidence: 99%

Regression models for exceedance data via the full likelihood

2010

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“…This has been found to be a flexible model in a range of applications (Tawn, 1988;Coles and Tawn, 1991;1994;Smith et al, 1994) with a parameter which controls the level of dependence, a = 0 and 1 corresponding to perfect dependence and independence respectively.…”

Section: The Faster Marginal Convergence Casementioning

confidence: 99%

“…However, in accordance with our aim to model the joint tail only, no model is specified for F~ when x <Um and an empirical esti- Coles and Tawn (1991;1994) and Joe et aL (1992) who argue that Fj can be treated as exact since below Urnj the data are relatively dense. The contribution to the likelihood of points in region f~] is obtained using an identical treatment to that of Section 2.3.…”

Section: Other Convergence Casesmentioning

confidence: 99%

“…Correspondingly ~b can be estimated given p. As A~ will typically contain regions beyond the range of the data, a parametric model for the tail of the joint density is required. Coles and Tawn (1991) and Smith et al (1994) propose models based on characterizations of the joint tail due to 0960-3174 9 1995 Chapman & Hall de Haan (1985) and Resnick (1987), respectively. The proposals make the following assumptions: characteristics, and there is no reason for both of these limiting approximations to hold above the same thresholds.…”

Section: Introductionmentioning

confidence: 99%

“…Let Mj, n = max(Xl,j,...,Xn,j) be the maximum of an independent and identically distributed sample of size n of the jth variable, and let F be the joint distribution function of Xwithjth marginal Fj. The models of Coles and Tawn (1991) and Smith et al (1994) are based on the limiting result P{ [MI,n -al,n]/bl,, <-Xl, . .…”

Section: Introductionmentioning

confidence: 99%

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A semi-parametric model for multivariate extreme values

Dixon

Tawn

1995

Stat Comput

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Threshold methods for multivariate extreme values are based on the use of asymptotically justified approximations of both the marginal distributions and the dependence structure in the joint tail. Models derived from these approximations are fitted to a region of the observed joint tail which is determined by suitably chosen high thresholds. A drawback of the existing methods is the necessity for the same thresholds to be taken for the convergence of both marginal and dependence aspects, which can result in inefficient estimation. In this paper an extension of the existing models, which removes this constraint, is proposed. The resulting model is semi-parametric and requires computationally intensive techniques for likelihood evaluation. The methods are illustrated using a coastal engineering application.

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