Estimating the Hüsler–Reiss variogram matrix by clipped moments

Shuang Hu () and Johan Segers ()
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Johan Segers: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2026029, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: In multivariate extreme value analysis, the tail dependence between some of the risk variables at hand may be weak, even when other variables do tend tobecome large simultaneously. Weak tail dependence may induce a substantial bias in estimation procedures based on the limiting multivariate (generalized) Pareto distribution of excesses over high thresholds. We consider a Hüsler–Reiss multivariate generalized Pareto model and, motivated by this issue, propose first- and second-order moment estimators of its variogram matrix constructed from a lower-tail-clipped version of the underlying random vector. The asymptotic normality of the proposed estimators is established. We demonstrate by simulation studies that they have lower bias than the empirical variogram estimator in certain cases, particularly when the dependence between components is weak. The estimators are applied to flood discharge data from the Danube river basin and the US flight delay data, showing that the tail dependence structure implied by the fitted model based on the first-order clipped moment estimator aligns more closely with the empirical tail dependence of the data than that based on the empirical variogram estimator.

Keywords: Hüsler–Reiss distribution; Variogram matrix; Moment estimator (search for similar items in EconPapers)
Pages: 55
Date: 2026-07-23
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvad:2026029

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