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Nonparametric adaptive inference of birth and death models in a large population limit

hal.structure.identifierR&D Milliman
dc.contributor.authorBoumezoued, Alexandre
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorHoffmann, Marc
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorJeunesse, Paulien
dc.date.accessioned2021-11-29T09:55:58Z
dc.date.available2021-11-29T09:55:58Z
dc.date.issued2021
dc.identifier.issn2520-2316
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22278
dc.language.isoenen
dc.subjectAge-structured modelsen
dc.subjectlarge population limiten
dc.subjectconcentration inequalitiesen
dc.subjectnonparametric adaptive estimationen
dc.subjectanisotropic estimationen
dc.subjectGoldenshluger–Lepski methoden
dc.subject.ddc519en
dc.titleNonparametric adaptive inference of birth and death models in a large population limiten
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenMotivated by improving mortality tables from human demography databases, we investigate statistical inference of a stochastic age-evolving density of a population alimented by time inhomogeneous mortality and fertility. Asymptotics are taken as the size of the population grows within a limited time horizon: the observation gets closer to the solution of the Von Foerster Mc Kendrick equation, and the difficulty lies in controlling simultaneously the stochastic approximation to the limiting PDE in a suitable sense together with an appropriate parametrisation of the anisotropic solution. In this setting, we prove new concentration inequalities that enable us to implement the Goldenshluger-Lepski algorithm and derive oracle inequalities. We obtain minimax optimality and adaptation over a wide range of anisotropic H\"older smoothness classes.en
dc.relation.isversionofjnlnameMathematical Statistics and Learning
dc.relation.isversionofjnlvol3en
dc.relation.isversionofjnlissue1en
dc.relation.isversionofjnldate2021-03
dc.relation.isversionofjnlpages1-69en
dc.relation.isversionofdoi10.4171/MSL/18en
dc.relation.isversionofjnlpublisherEuropean mathematical societyen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenon
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2021-11-29T09:50:02Z
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