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Annals of the Institute of Statistical Mathematics

, Volume 68, Issue 5, pp 1135–1162 | Cite as

Kernel regression with Weibull-type tails

  • Tertius de Wet
  • Yuri GoegebeurEmail author
  • Armelle Guillou
  • Michael Osmann
Article
  • 226 Downloads

Abstract

We consider the estimation of the tail coefficient of a Weibull-type distribution in the presence of random covariates. The approach followed is non-parametric and consists of locally weighted estimation in narrow neighbourhoods in the covariate space. We introduce two families of estimators and study their asymptotic behaviour under some conditions on the conditional response distribution, the kernel function, the density function of the independent variables, and for appropriately chosen bandwidth and threshold parameters. We also introduce a Weissman-type estimator for estimating upper extreme conditional quantiles. The finite sample behaviour of the proposed estimators is examined with a simulation experiment. The practical applicability of the methodology is illustrated on a dataset of sea storm measurements.

Keywords

Extreme value statistics Weibull-type distribution Regression Second-order condition 

Notes

Acknowledgments

The authors kindly acknowledge Laurens de Haan and Ana Ferreira for providing the sea level data. This work was supported by a research Grant (VKR023480) from VILLUM FONDEN and an international project for scientific cooperation (PICS-6416). The authors are very grateful to the editor and two anonymous referees for their helpful and constructive comments on the preliminary versions of the paper.

Supplementary material

10463_2015_531_MOESM1_ESM.pdf (205 kb)
Supplementary material 1 (pdf 204 KB)

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Copyright information

© The Institute of Statistical Mathematics, Tokyo 2015

Authors and Affiliations

  • Tertius de Wet
    • 1
  • Yuri Goegebeur
    • 2
    Email author
  • Armelle Guillou
    • 3
  • Michael Osmann
    • 2
  1. 1.Department of Statistics and Actuarial ScienceUniversity of StellenboschStellenboschSouth Africa
  2. 2.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdense MDenmark
  3. 3.Institut Recherche Mathématique Avancée, UMR 7501Université de Strasbourg et CNRSStrasbourg CedexFrance

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