Abstract
In this paper, and in a context of regularly varying tails, we propose different alternatives to a well-known estimator of the tail index—the Hill estimator (Hill, 1975). These alternatives have essentially in mind a reduction in bias, preferably without increasing Mean Square Error, by the use of suitable Generalized Jackknife methodologies (Gray and Schucany, 1972). The first estimate obtained through this methodolgy is the one introduced by Peng (1998), under a different context. Other Generalized Jackknife estimators are linear combinations of Hill estimators at different levels. This methodology of affine combinations of Hill estimators at different levels may be easily generalized to other semi-parametric estimators of the tail index, like Pickands' estimator (Pickands, 1975) or the Moment's estimator (Dekkers et al., 1989), and consequently to a general real tail index, seeming to be a promising field of research.
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Ivette Gomes, M., João Martins, M. & Neves, M. Alternatives to a Semi-Parametric Estimator of Parameters of Rare Events—The Jackknife Methodology*. Extremes 3, 207–229 (2000). https://doi.org/10.1023/A:1011470010228
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DOI: https://doi.org/10.1023/A:1011470010228