Penalized maximum likelihood and semiparametric second-order efficiency

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dc.creatorDalalyan, A. S.
dc.creatorGolubev, G. K.
dc.creatorTsybakov, A. B.
dc.date2006-05-16
dc.date.accessioned2026-07-07T08:07:48Z
dc.date.available2026-07-07T08:07:48Z
dc.descriptionWe consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that second-order efficiency is crucial in semiparametric problems since only the second-order terms in asymptotic expansion for the risk account for the behavior of the ``nonparametric component'' of a semiparametric procedure, and they are not dramatically smaller than the first-order terms.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053605000000895 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0605437
dc.identifierhttp://arxiv.org/abs/math/0605437
dc.identifierAnnals of Statistics 2006, Vol. 34, No. 1, 169-201
dc.identifierdoi:10.1214/009053605000000895
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131055
dc.subjectStatistics Theory
dc.subject62G05, 62G20 (Primary)
dc.titlePenalized maximum likelihood and semiparametric second-order efficiency
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