Improved reduced-bias tail index and quantile estimators
By Jan Beirlant, Fernanda Otilia Figueiredo, M. Ivette Gomes, B. Vandewalle. 2008
49 citations recorded by the source corpus.
Abstract In this paper, we deal with bias reduction techniques for heavy tails, trying to improve mainly upon the performance of classical high quantile estimators. High quantiles depend strongly on the tail index γ , for which new classes of reduced-bias estimators have recently been introduced, where the second-order parameters in the bias are estimated at a level k 1 of a larger order than the level k at which the tail index is estimated. Doing this, it was seen that the asymptotic variance of the new estimators could be kept equal to the one of the popular Hill estimators. In a similar way, we now introduce new classes of tail index and associated high quantile estimators, with an asymptotic mean squared error smaller than that of the classical ones for all k in a large class of heavy-tailed models. We derive their asymptotic distributional properties and compare them with those of alternative estimators. Next to that, an illustration of the finite sample behavior of the estimators is also provided through a Monte Carlo simulation study and the application to a set of real data in the field of insurance.
Subfields: Demography, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/91fb90fec7cb3ee045fc8f974ade3a6bfcea45de
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In Demography
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Citations in the corpus
- Bias correction in extreme value statistics with index around zero (2013, background): “To our best knowledge, bias correction for high quantile estimators has been studied for the γ positive case only; see e.g. Matthys et al. (2004), Gomes and Figueiredo (2006), Gomes and Pestana (2007a), Beirlant et al. (2008) and Li et al. (2010b).”