A Mean-of-Order-\(p\) Class of Value-at-Risk Estimators

  • M. Ivette GomesEmail author
  • M. Fátima Brilhante
  • Dinis Pestana
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 136)


The main objective of statistics of univariate extremes lies in the estimation of quantities related to extreme events. In many areas of application, like finance, insurance and statistical quality control, a typical requirement is to estimate a high quantile, i.e. the Value at Risk at a level \(q (\)VaR\(_q)\), high enough, so that the chance of exceedance of that value is equal to \(q\), with \(q\) small. In this paper we deal with the semi-parametric estimation of VaR\(_q\), for heavy tails, introducing a new class of VaR-estimators based on a class of mean-of-order- \(p\) (MOP) extreme value index (EVI)-estimators, recently introduced in the literature. Interestingly, the MOP EVI-estimators can have a mean square error smaller than that of the classical EVI-estimators, even for small values of \(k\). They are thus a nice basis to build alternative VaR-estimators not only around optimal levels, but for other levels too.The new VaR-estimators are compared with the classical ones, not only asymptotically, but also for finite samples, through Monte-Carlo techniques.


Heavy right tails Semi-parametric estimation Statistics of extremes Value-at-risk estimation 



Research partially supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, projects PEst-OE /MAT /UI0006 /2011, 2014 (CEAUL) and EXTREMA, PTDC /MAT /101736 /2008.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • M. Ivette Gomes
    • 1
    • 2
    Email author
  • M. Fátima Brilhante
    • 1
    • 3
  • Dinis Pestana
    • 1
    • 2
  1. 1.Centro de Estatística e Aplicações, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal
  2. 2.Instituto de Investigação Científica Bento da Rocha CabralLisbonPortugal
  3. 3.Universidade dos Açores (DM)Ponta DelgadaPortugal

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