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

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 p...

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Bibliographic Details
Published in:Journal of statistical computation and simulation 2015-11, Vol.85 (17), p.3405-3419
Main Authors: Caeiro, Frederico, Gomes, M. Ivette
Format: Article
Language:English
Subjects:
Bias
Computer simulation
Convergence
Estimating techniques
Estimators
Extreme values
Mathematical models
Monte Carlo methods
Monte Carlo simulation
Statistics
Tuning
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Summary: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.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2014.975707