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Régression quantile extrême : une approche par couplage et distance de Wasserstein.

Abstract : This work is related with the estimation of conditional extreme quantiles. More precisely, we estimate high quantiles of a real distribution conditionally to the value of a covariate, potentially in high dimension. A such estimation is made introducing the proportional tail model. This model is studied with coupling methods. The first is an empirical processes based method whereas the second is focused on transport and optimal coupling. We provide estimators of both quantiles and model parameters, we show their asymptotic normality with our coupling methods. We also provide a validation procedure for proportional tail model. Moreover, we develop the second approach in the general framework of univariate extreme value theory.
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https://tel.archives-ouvertes.fr/tel-03156028
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Submitted on : Tuesday, March 2, 2021 - 11:07:09 AM
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Benjamin Bobbia. Régression quantile extrême : une approche par couplage et distance de Wasserstein.. Statistiques [math.ST]. Université Bourgogne Franche-Comté, 2020. Français. ⟨NNT : 2020UBFCD043⟩. ⟨tel-03156028⟩

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