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Non-parametric estimator of a multivariate madogram for missing-data and extreme value framework

Abstract : The modeling of dependence between maxima is an important subject in several applications in risk analysis. To this aim, the extreme value copula function, characterised via the madogram, can be used as a margin-free description of the dependence structure. From a practical point of view, the family of extreme value distributions is very rich and arise naturally as the limiting distribution of properly normalised component-wise maxima. In this paper, we investigate the nonparametric estimation of the madogram where data are completely missing at random. We provide the functional central limit theorem for the considered multivariate madrogram correctly normalized, towards a tight Gaussian process for which the covariance function depends on the probabilities of missing. Explicit formula for the asymptotic variance is also given. Our results are illustrated in a finite sample setting with a simulation study.
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https://hal.archives-ouvertes.fr/hal-03502804
Contributor : Alexis Boulin Connect in order to contact the contributor
Submitted on : Friday, April 29, 2022 - 10:08:03 AM
Last modification on : Tuesday, October 25, 2022 - 4:16:16 PM

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Alexis Boulin, Elena Di Bernardino, Thomas Laloë, Gwladys Toulemonde. Non-parametric estimator of a multivariate madogram for missing-data and extreme value framework. Journal of Multivariate Analysis, 2022, Journal of Multivariate Analysis 192 (2022), 192, ⟨10.1016/j.jmva.2022.105059⟩. ⟨hal-03502804v2⟩

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