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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
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 functional 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 distributions 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 simultaneous confidence set for the cumulative hazard function based on the Nelson–Aalen estimator and investigate a problem in stochastic programming related to computational 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.doi10.3103/S106653071104003X


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