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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorBelhakem, Mohammed Ryad
hal.structure.identifierLaboratoire de biologie et modélisation de la cellule [LBMC UMR 5239]
dc.contributor.authorPicard, Franck
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorRivoirard, Vincent
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorRoche, Angelina
dc.date.accessioned2022-02-28T11:38:04Z
dc.date.available2022-02-28T11:38:04Z
dc.date.issued2021
dc.identifier.urihttps://basepub.dauphine.psl.eu/handle/123456789/22799
dc.language.isoenen
dc.subjectFunctional data analysis
dc.subjectPrincipal Components Analysis
dc.subjectminimax rates
dc.titleMinimax estimation of Functional Principal Components from noisy discretized functional dataen
dc.typeDocument de travail / Working paper
dc.description.abstractenFunctional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise. However, functional data are noisy and necessarily observed on a finite discretization grid. Common practice consists in smoothing the data and then to compute the functional estimates, but the impact of this denoising step on the procedure’s statistical performance are rarely considered. Here we prove new convergence rates for functional principal component estimators. We introduce a double asymptotic framework: one corresponding to the sampling size and a second to the size of the grid. We prove that estimates based on projection onto histograms show optimal rates in a minimax sense. Theoretical results are illustrated on simulated data and the method is applied to the visualization of genomic data.
dc.publisher.cityParisen
dc.identifier.citationpages35en
dc.relation.ispartofseriestitleCahier de recherche CEREMADE, Université Paris Dauphine-PSLen
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-03395522
dc.identifier.citationdate2021
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dc.description.audienceInternational
dc.date.updated2022-02-28T11:24:12Z
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