NDLI: Kernel estimators of extreme level curves

Content Provider	Springer Nature Link
Author	Daouia, Abdelaati Gardes, Laurent Girard, Stéphane Lekina, Alexandre
Copyright Year	2010
Abstract	We address the estimation of extreme level curves of heavy-tailed distributions. This problem is equivalent to estimating quantiles when covariate information is available and when their order converges to one as the sample size increases. We show that, under some conditions, these so-called “extreme conditional quantiles” can still be estimated through a kernel estimator of the conditional survival function. Sufficient conditions on the rate of convergence of their order to one are provided to obtain asymptotically Gaussian distributed estimators. Making use of this result, some kernel estimators of the conditional tail-index are introduced and a Weissman type estimator is derived, permitting to estimate extreme conditional quantiles of arbitrary large order. These results are illustrated through simulated and real datasets.
Starting Page	311
Ending Page	333
Page Count	23
File Format	PDF
ISSN	11330686
Journal	Test
Volume Number	20
Issue Number	2
e-ISSN	18638260
Language	English
Publisher	Springer-Verlag
Publisher Date	2010-06-06
Publisher Institution	Spanish Society of Statistics and Operations Research
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Conditional quantiles Heavy-tail distributions Kernel estimator Extreme-values Statistics of extreme values; tail inference Order statistics; empirical distribution functions Asymptotic distribution theory Statistics Statistical Theory and Methods Statistics for Business/Economics/Mathematical Finance/Insurance
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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