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, Volume 20, Issue 2, pp 311–333 | Cite as

Kernel estimators of extreme level curves

  • Abdelaati Daouia
  • Laurent Gardes
  • Stéphane Girard
  • Alexandre Lekina
Original Paper

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.

Keywords

Conditional quantiles Heavy-tail distributions Kernel estimator Extreme-values 

Mathematics Subject Classification (2000)

62G32 62G30 62E20 

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2010

Authors and Affiliations

  • Abdelaati Daouia
    • 1
  • Laurent Gardes
    • 2
  • Stéphane Girard
    • 2
  • Alexandre Lekina
    • 2
  1. 1.Toulouse School of Economics (GREMAQ)University of ToulouseToulouseFrance
  2. 2.INRIA Rhône-Alpes, Team MistisSaint-Ismier cedexFrance

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