On the errors committed by sequences of estimator functionals
Journal article, Peer reviewed
Permanent lenke
http://hdl.handle.net/11250/93872Utgivelsesdato
2011Metadata
Vis full innførselSamlinger
- Scientific articles [1211]
Originalversjon
http://dx.doi.org/10.3103/S106653071104003XSammendrag
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
Beskrivelse
This is the authors’ final, accepted and refereed manuscript to the article. The final publication is available at www.springerlink.com