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Tail index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses

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Summary. 

We are interested in the derivation of the distributional properties of a weighted log-excesses estimator of a positive tail index γ. One of the main objectives of such an estimator is the accommodation of the dominant component of asymptotic bias, together with the maintenance of the asymptotic variance of the maximum likelihood estimator of γ, under a strict Pareto model. We consider the external estimation not only of a second-order shape parameter but also of a second-order scale parameter β. This will enable us to reduce the asymptotic variance of the final estimators under consideration, compared with second-order reduced bias estimators that are already available in the literature. The second-order reduced bias estimators that are considered are also studied for finite samples, through Monte Carlo techniques, as well as applied to real data in the field of finance.
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Keywords: Heavy tails; Log-excesses; Maximum likelihood; Semiparametric estimation; Statistics of extremes

Document Type: Research Article

Affiliations: 1: Universidade de Lisboa, Portugal 2: Erasmus University of Rotterdam, The Netherlands, and Universidade de Lisboa, Portugal 3: Instituto Politécnico de Tomar and Universidade de Lisboa, Portugal

Publication date: February 1, 2008

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