dc.contributor.author | Grønneberg, Steffen | |
dc.contributor.author | Hjort, Nils Lid | |
dc.date.accessioned | 2013-08-07T12:52:06Z | |
dc.date.available | 2013-08-07T12:52:06Z | |
dc.date.issued | 2011 | |
dc.identifier.issn | 1934-8045 (e-utg) | |
dc.identifier.uri | http://hdl.handle.net/11250/93872 | |
dc.description | This is the authors’ final, accepted and refereed manuscript to the article. The final publication is available at www.springerlink.com | no_NO |
dc.description.abstract | Consider 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 complexity | no_NO |
dc.language.iso | eng | no_NO |
dc.publisher | Springer | no_NO |
dc.subject | the last n | no_NO |
dc.subject | Hadamard-differentiable statistical functionals | no_NO |
dc.subject | sequential confidence regions | no_NO |
dc.subject | Gaussian processes | no_NO |
dc.subject | Nelson–Aalen estimator | no_NO |
dc.title | On the errors committed by sequences of estimator functionals | no_NO |
dc.type | Journal article | no_NO |
dc.type | Peer reviewed | no_NO |
dc.source.pagenumber | 327-346 | no_NO |
dc.source.volume | 20 | no_NO |
dc.source.journal | Mathematical Methods of Statistics | no_NO |
dc.source.issue | 4 | no_NO |
dc.identifier.doi | http://dx.doi.org/10.3103/S106653071104003X | |