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dc.contributor.authorDoumic, Marie
dc.contributor.authorHoffmann, Marc
dc.contributor.authorKrell, Nathalie
dc.contributor.authorRobert, Lydia
dc.date.accessioned2018-01-09T10:33:43Z
dc.date.available2018-01-09T10:33:43Z
dc.date.issued2015
dc.identifier.issn1350-7265
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17255
dc.language.isoenen
dc.subjectNonparametric estimationen
dc.subjectGrowth-fragmentationen
dc.subjectcell division equationen
dc.subjectMarkov chain on a treeen
dc.subject.ddc519en
dc.titleStatistical estimation of a growth-fragmentation model observed on a genealogical treeen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe raise the issue of estimating the division rate for a growing and dividing population modelled by a piecewise deterministic Markov branching tree. Such models have broad applications, ranging from TCP/IP window size protocol to bacterial growth. Here, the individ-uals split into two offsprings at a division rate B(x) that depends on their size x, whereas their size grow exponentially in time, at a rate that exhibits variability. The mean empirical measure of the model satisfies a growth-fragmentation type equation, and we bridge the determinis-tic and probabilistic viewpoints. We then construct a nonparametric estimator of the division rate B(x) based on the observation of the pop-ulation over different sampling schemes of size n on the genealogical tree. Our estimator nearly achieves the rate n −s/(2s+1) in squared-loss error asymptotically, generalizing and improving on the rate n −s/(2s+3) obtained in [13, 15] through indirect observation schemes. Our method is consistently tested numerically and implemented on Escherichia coli data, which demonstrates its major interest for practical applications.en
dc.relation.isversionofjnlnameBernoulli
dc.relation.isversionofjnlvol21en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages1760-1799en
dc.relation.isversionofdoi10.3150/14-BEJ623en
dc.relation.isversionofjnlpublisherInternational Statistical Instituteen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-01-09T10:26:57Z
hal.person.labIds25
hal.person.labIds60
hal.person.labIds75
hal.person.labIds132919


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