Structural adaptation via $L_p$-norm oracle inequalities

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dc.creatorGoldenhsluger, A.
dc.creatorLepski, O.
dc.date2007-04-19
dc.date.accessioned2026-07-07T07:57:19Z
dc.date.available2026-07-07T07:57:19Z
dc.descriptionIn this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary $\rL_p$--losses. These results are applied for adaptive estimation in the additive multi--index model.
dc.identifierhttps://arxiv.org/abs/0704.2492
dc.identifierhttp://arxiv.org/abs/0704.2492
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127605
dc.subjectStatistics Theory
dc.subjectProbability
dc.subject62G05, 62G20
dc.titleStructural adaptation via $L_p$-norm oracle inequalities
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