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dc.contributor.authorMeziani, Katia
HAL ID: 2110
dc.contributor.authorButucea, Cristina
dc.subjectSecond order risken
dc.subjectQuadratic functionalen
dc.subjectProjection estimatoren
dc.subjectPinsker estimatoren
dc.subjectParametric rateen
dc.subjectMinimax upper boundsen
dc.subjectInverse problemen
dc.subjectGaussian sequence modelen
dc.titleQuadratic functional estimation in inverse problemsen
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherLaboratoire de Mathématiques Paul Painlevé CNRS : UMR8524 – Université Lille 1;France
dc.description.abstractenIn 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.isversionofjnlnameStatistical Methodology
dc.subject.ddclabelProbabilités et mathématiques appliquéesen

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