Trimming and threshold selection in extremes

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Serval ID
serval:BIB_0FE1CD5C80A1
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
Trimming and threshold selection in extremes
Journal
Extremes
Author(s)
Bladt M., Albrecher H., Beirlant J.
ISSN
1386-1999
Publication state
Published
Issued date
2020
Peer-reviewed
Oui
Volume
23
Number
5
Pages
629-665
Language
english
Abstract
We consider removing lower order statistics from the classical
Hill estimator in extreme value statistics, and compensating for it by rescaling
the remaining terms. Trajectories of these trimmed statistics as a function of
the extent of trimming turn out to be quite flat near the optimal threshold
value. For the regularly varying case, the classical threshold selection problem
in tail estimation is then revisited, both visually via trimmed Hill plots and,
for the Hall class, also mathematically via minimizing the expected empirical
variance. This leads to a simple threshold selection procedure for the classical
Hill estimator which circumvents the estimation of some of the tail character-
istics, a problem which is usually the bottleneck in threshold selection. As a
by-product, we derive an alternative estimator of the tail index, which assigns
more weight to large observations, and works particularly well for relatively
lighter tails. A simple ratio statistic routine is suggested to evaluate the good-
ness of the implied selection of the threshold. We illustrate the favourable
performance and the potential of the proposed method with simulation studies and real insurance data.
Create date
29/06/2020 16:41
Last modification date
30/10/2020 6:23
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