dc.contributor.author Meziani, Katia HAL ID: 2110 dc.contributor.author Butucea, Cristina dc.date.accessioned 2011-10-26T14:18:38Z dc.date.available 2011-10-26T14:18:38Z dc.date.issued 2011 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/7339 dc.language.iso en en dc.subject Second order risk en dc.subject Quadratic functional en dc.subject Projection estimator en dc.subject Pinsker estimator en dc.subject Parametric rate en dc.subject Minimax upper bounds en dc.subject Inverse problem en dc.subject Gaussian sequence model en dc.subject.ddc 519 en dc.title Quadratic functional estimation in inverse problems en dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Laboratoire de Mathématiques Paul Painlevé CNRS : UMR8524 – Université Lille 1;France dc.description.abstracten In this paper, we consider a Gaussian sequence of independent observations having a polynomially increasing variance. This model describes a large panel of inverse problems, such as the deconvolution of blurred images or the recovering of the fractional derivative of a signal. We estimate the sum of squares of the means of our observations. This quadratic functional has practical meanings, e.g. the energy of a signal, and it is often used for goodness-of-fit testing. We compute Pinsker estimators when the underlying signal has both a finite and infinite amount of smoothness. When the signal is sufficiently smoother than the difficulty of the inverse problem, we attain the parametric rate and the efficiency constant associated with it. Moreover, we give upper bounds of the second order term in the risk. Otherwise, when the parametric rate cannot be attained, we compute non parametric upper bounds of the risk. en dc.relation.isversionofjnlname Statistical Methodology dc.relation.isversionofjnlvol 8 en dc.relation.isversionofjnlissue 1 en dc.relation.isversionofjnldate 2011 dc.relation.isversionofjnlpages 31-41 en dc.relation.isversionofdoi http://dx.doi.org/10.1016/j.stamet.2010.05.002 en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher Elsevier en dc.subject.ddclabel Probabilités et mathématiques appliquées en
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