Likelihood estimators for multivariate extremes

By Raphaël Huser, A. C. Davison, Marc G. Genton. 2014

68 citations recorded by the source corpus.

The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of componentwise maxima, high threshold exceedances or point processes, yielding different but related asymptotic characterizations and estimators. The present paper clarifies the connections between the main likelihood estimators, and assesses their practical performance. We investigate their ability to estimate the extremal dependence structure and to predict future extremes, using exact calculations and simulation, in the case of the logistic model.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d626fb5a437d7336877326e2d5c6fba2422e7e94

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Citations in the corpus

A continuous updating weighted least squares estimator of tail dependence in high dimensions (2016, methodology): “In Huser et al. (2016), a comprehensive comparison of likelihood estimators for θ has been performed based on random samples from this copula.”
Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures (2016, background): “s ˜ and ˜are represented by dots at u= 1. The left column displays an asymptotic dependent scenario, while the middle and right columns display asymptotic independence. fromThibaud and Opitz(2015) andHuser et al. (2016) suggest it provides a reasonable compromise between bias and variance compared t”
Functional peaks‐over‐threshold analysis (2020, background): “Maximum likelihood estimation of θW has been studied for specific risk functionals but can perform poorly because the limiting process is misspecified for finite un (Engelke & Malinowski, 2014; Huser et al., 2016).”
Multivariate peaks over thresholds models (2016, unknown): “Huser et al. (2015) explore the merits of this and other approaches via simulation.”
Modeling Spatial Processes with Unknown Extremal Dependence Class (2017, methodology): “Notice that margins are here available in closed form, unlike the Gaussian scale mixture model of Huser et al. (2017), or the bivariate model of Wadsworth et al.”