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dc.contributor.authorGrønneberg, Steffen
dc.contributor.authorHjort, Nils Lid
dc.date.accessioned2013-08-07T12:52:06Z
dc.date.available2013-08-07T12:52:06Z
dc.date.issued2011
dc.identifier.issn1934-8045 (e-utg)
dc.identifier.urihttp://hdl.handle.net/11250/93872
dc.descriptionThis is the authors’ final, accepted and refereed manuscript to the article. The final publication is available at www.springerlink.comno_NO
dc.description.abstractConsider a sequence of estimators ˆ n which converges almost surely to 0 as the sample size n tends to infinity. Under weak smoothness conditions, we identify the asymptotic limit of the last time ˆ n is further than " away from 0 when " → 0+. These limits lead to the construction of sequentially fixed width confidence regions for which we find analytic approximations. The smoothness conditions we impose is that ˆ n is to be close to a Hadamard-differentiable func- tional of the empirical distribution, an assumption valid for a large class of widely used statistical estimators. Similar results were derived in Hjort and Fenstad (1992, Annals of Statistics) for the case of Euclidean parameter spaces; part of the present contribution is to lift these results to situations involving parameter functionals. The apparatus we develop is also used to derive appropriate limit dis- tributions of other quantities related to the far tail of an almost surely convergent sequence of estimators, like the number of times the estimator is more than " away from its target. We illustrate our results by giving a new sequential simultane- ous confidence set for the cumulative hazard function based on the Nelson–Aalen estimator and investigate a problem in stochastic programming related to compu- tational complexityno_NO
dc.language.isoengno_NO
dc.publisherSpringerno_NO
dc.subjectthe last nno_NO
dc.subjectHadamard-differentiable statistical functionalsno_NO
dc.subjectsequential confidence regionsno_NO
dc.subjectGaussian processesno_NO
dc.subjectNelson–Aalen estimatorno_NO
dc.titleOn the errors committed by sequences of estimator functionalsno_NO
dc.typeJournal articleno_NO
dc.typePeer reviewedno_NO
dc.source.pagenumber327-346no_NO
dc.source.volume20no_NO
dc.source.journalMathematical Methods of Statisticsno_NO
dc.source.issue4no_NO
dc.identifier.doihttp://dx.doi.org/10.3103/S106653071104003X


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