Bias reduction in the estimation of a shape second-order parameter of a heavy-tailed model

Frederico Caeiro, M. Ivette Gomes

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)


In extreme value theory, the shape second-order parameter is a quite relevant parameter related to the speed of convergence of maximum values, linearly normalized, towards its limit law. The adequate estimation of this parameter is vital for improving the estimation of the extreme value index, the primary parameter in statistics of extremes. In this article, we consider a recent class of semi-parametric estimators of the shape second-order parameter for heavy right-tailed models. These estimators, based on the largest order statistics, depend on a real tuning parameter, which makes them highly flexible and possibly unbiased for several underlying models. In this article, we are interested in the adaptive choice of such tuning parameter and the number of top order statistics used in the estimation procedure. The performance of the methodology for the adaptive choice of parameters is evaluated through a Monte Carlo simulation study.

Original languageEnglish
Pages (from-to)3405-3419
Number of pages15
JournalJournal of Statistical Computation and Simulation
Issue number17
Publication statusPublished - 2015


  • bias reduction
  • heavy tails
  • second-order parameter
  • semi-parametric estimation


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