Benjamin Bobbia; Clément Dombry; Davit Varron
The coupling method in extreme value theory Journal Article
In: Bernoulli, vol. 27, no. 3, pp. 1824-1850, 2021.
@article{bobbia_1682,
title = {The coupling method in extreme value theory},
author = {Benjamin Bobbia and Clément Dombry and Davit Varron},
url = {https://projecteuclid.org/journals/bernoulli/volume-27/issue-3/The-coupling-method-in-extreme-value-theory/10.3150/20-BEJ1293.short},
year = {2021},
date = {2021-08-01},
journal = {Bernoulli},
volume = {27},
number = {3},
pages = {1824-1850},
abstract = {A coupling method is developed for univariate extreme value theory, providing an alternative to the use of the tail empirical/quantile processes. We emphasize the Peak-over-Threshold approach that approximates the distribution above high threshold by the Generalized Pareto Distribution (GPD) and compare the empirical distribution of exceedances to the empirical distribution associated with the limit GPD model. Sharp bounds for their Wasserstein distance in the second order Wasserstein space are provided. As an application, we recover standard results on the asymptotic behavior of the Hill estimator, the Weissman extreme quantile estimator or the probability weighted moment estimators, shedding some new light on the theory.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Benjamin Bobbia; Clément Dombry; Davit Varron
Extreme quantile regression in proportional tail framework Journal Article
In: Transactions of A. Razmadze Mathematical Institute, In press, vol. 175, no. 1, pp. 13-32, 2021.
@article{bobbia_1684,
title = {Extreme quantile regression in proportional tail framework},
author = {Benjamin Bobbia and Clément Dombry and Davit Varron},
url = {http://rmi.ge/transactions/TRMI-volumes/175-1/175-1.htm},
year = {2021},
date = {2021-04-01},
journal = {Transactions of A. Razmadze Mathematical Institute, In press},
volume = {175},
number = {1},
pages = {13-32},
abstract = {We revisit the model of heteroscedastic extremes initially introduced by Einmahl et al. (JRSSB, 2016) to describe the evolution of a non stationary sequence whose extremes evolve over time and adapt it into a general extreme quantile regression framework. We provide estimates for the extreme value index and the integrated skedasis function and prove their asymptotic normality. Our results are quite similar to those developed for heteroscedastic extremes but with a different proof approach emphasizing coupling arguments. We also propose a pointwise estimator of the skedasis function and a Weissman estimator of the conditional extreme quantile and prove the asymptotic normality of both estimators.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Benjamin Bobbia
Théorème de Donsker pour des mesures empiriques locales sur des régions aléatoires Conference
53-ème journées de statistique, Lyon, France, 2022.
@conference{bobbia_1855,
title = {Théorème de Donsker pour des mesures empiriques locales sur des régions aléatoires},
author = {Benjamin Bobbia},
year = {2022},
date = {2022-06-01},
booktitle = {53-ème journées de statistique},
address = {Lyon, France},
abstract = {Nowadays, empirical processes are well known objects. A reason that push forward theirs studies is that, in many models, we can write the estimators as images of empirical measures. In this work we investigate the case of local empirical measures built over a sub-sample with data conditioned to be in a certain area. There exists numerous results about such question, but what can we say if the area of interest is data driven ? In the present work we present a general framework which allows to derive asymptotic results for this particular empirical measures (with "low" cost in terms of technicality and assumptions). This approach is mainly presented through the prism of extreme values theory. And we present an example illustrating how this empirical conditional measure assumption work well with optimal transport methods.},
keywords = {},
pubstate = {accepted},
tppubtype = {conference}
}
Benjamin Bobbia
A Dansker's Theorem for data driven local empirical measures Conference
Séminaire de l'équipe S2A Télécom Paris, Palaiseau, France, 2022.
@conference{bobbia_1856,
title = {A Dansker's Theorem for data driven local empirical measures},
author = {Benjamin Bobbia},
year = {2022},
date = {2022-03-01},
booktitle = {Séminaire de l'équipe S2A Télécom Paris},
address = {Palaiseau, France},
abstract = {Nowadays, empirical processes are well known objects. A reason that push forward theirs studies is that, in many models, we can write the estimators as images of empirical measures. In this work we investigate the case of local empirical measures built over a sub-sample with data conditioned to be in a certain area. There exists numerous results about such question, but what can we say if the area of interest is data driven ? In the present work we present a general framework which allows to derive asymptotic results for this particular empirical measures (with "low" cost in terms of technicality and assumptions). In this talk, this approach is specified for the framework of extreme values theory. In which we presente how tail and quantile estimation can be derived from a such methodology.},
keywords = {},
pubstate = {accepted},
tppubtype = {conference}
}
Benjamin Bobbia
Donsker's Theorem for local Data-Driven Empirical Measure Conference
Séminaire du laboratoire Modal X, Nanterre, France, 2022.
@conference{bobbia_1773,
title = {Donsker's Theorem for local Data-Driven Empirical Measure},
author = {Benjamin Bobbia},
url = {x},
year = {2022},
date = {2022-02-01},
booktitle = {Séminaire du laboratoire Modal X},
address = {Nanterre, France},
abstract = {Nowadays, empirical processes are well known objects. A reason that push forward theirs studies is that, in many models, we can write the estimators as images of empirical measures. In this work we investigate the case of local empirical measures built over a sub-sample with data conditioned to be in a certain area. There exists numerous results about such question, but what can we say if the area of interest is data driven ? In the present work we present a general framework which allows to derive asymptotic results for this particular empirical measures (with "low" cost in terms of technicality and assumptions). Then, we use this approach in the framework of extreme values theory deriving tail and quantile estimations.},
keywords = {},
pubstate = {published},
tppubtype = {conference}
}
Benjamin Bobbia
Donsker's Theorem for local data-driven empirical measures Conference
Forum Jeunes Mathématiciens, Besançon, france, 2021.
@conference{bobbia_1772,
title = {Donsker's Theorem for local data-driven empirical measures},
author = {Benjamin Bobbia},
url = {https://femmes-et-maths.fr/2021/06/28/forum-2021-des-jeunes-mathematien-nes/},
year = {2021},
date = {2021-12-01},
booktitle = {Forum Jeunes Mathématiciens},
address = {Besançon, france},
abstract = {Nowadays, empirical processes are well known object. A reason that push forward theirs studies is that, in many modelisations, we can write the estimators as images of empirical measures. In this work we investigate the case of local empirical measures, that is the empirical measure built over a subsample with data conditionned to be in a certain area. There exist numerous results about such result, but what can we say if the previous area is data driven ? We can handle this situation with high technical cost and additional assumptions. The main aim of the present work is to present a general framework which allows to derive asymptotic results for this particular empirical measures with lower cost (in terms of technicality and assumptions). We give a Donsker-type theorem for such measures and present some domains of application as extreme values theory or multivariate regular variations},
keywords = {},
pubstate = {published},
tppubtype = {conference}
}
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