Benjamin Bobbia

@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}

}

@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}

}

@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}

}

@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}

}