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Extremes

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Bias-corrected estimation for conditional Pareto-type distributions with random right censoring

  • Yuri GoegebeurEmail author
  • Armelle Guillou
  • Jing Qin
Article

Abstract

We consider bias-reduced estimation of the extreme value index in conditional Pareto-type models with random covariates when the response variable is subject to random right censoring. The bias-correction is obtained by fitting the extended Pareto distribution locally to the relative excesses over a high threshold using the maximum likelihood method. Convergence in probability and asymptotic normality of the estimators are established under suitable assumptions. The finite sample behaviour is illustrated with a simulation experiment and the method is applied to two real datasets.

Keywords

Pareto-type model Random covariate Random right censoring Local estimation Bias-reduction 

AMS 2000 Subject Classifications

62G08 62G20 62G32 

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Notes

Acknowledgements

This work was supported by a research grant (VKR023480) from VILLUM FONDEN. Computation/simulation for the work described in this paper was supported by the DeIC National HPC Centre, SDU. The authors sincerely thank the editor, associate editor and the referees for their helpful comments and suggestions that led to substantial improvement of the paper. The authors also take pleasure in thanking Gilles Stupfler for providing the code to compute the estimator proposed in Stupfler (2016).

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceUniversity of Southern DenmarkOdenseDenmark
  2. 2.Institut Recherche Mathématique Avancée, UMR 7501Université de Strasbourg et CNRSStrasbourg cedexFrance

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