Publicação
Direct Reduction of Bias of the Classical Hill Estimator
| Resumo: | In this paper we are interested in an adequate estimation of the dominant component of the bias of Hill’s estimator of a positive tail index γ, in order to remove it from the classical Hill estimator in different asymptotically equivalent ways. If the second order parameters in the bias are computed at an adequate level k1 of a larger order than that of the level k at which the Hill estimator is computed, there may be no change in the asymptotic variances of these reduced bias tail index estimators, which are kept equal to the asymptotic variance of the Hill estimator, i.e., equal to γ 2 . The asymptotic distributional properties of the proposed estimators of γ are derived and the estimators are compared not only asymptotically, but also for finite samples through Monte Carlo techniques. |
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| Autores principais: | Caeiro, Frederico Almeida Gião Gonçalves |
| Outros Autores: | Gomes, M. Ivette; Pestana, Dinis |
| Assunto: | bias estimation semi-parametric estimation heavy tails statistics of extremes statistics of Extremes semi-parametric estimation bias estimation heavy tails |
| Ano: | 2005 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| Resumo: | In this paper we are interested in an adequate estimation of the dominant component of the bias of Hill’s estimator of a positive tail index γ, in order to remove it from the classical Hill estimator in different asymptotically equivalent ways. If the second order parameters in the bias are computed at an adequate level k1 of a larger order than that of the level k at which the Hill estimator is computed, there may be no change in the asymptotic variances of these reduced bias tail index estimators, which are kept equal to the asymptotic variance of the Hill estimator, i.e., equal to γ 2 . The asymptotic distributional properties of the proposed estimators of γ are derived and the estimators are compared not only asymptotically, but also for finite samples through Monte Carlo techniques. |
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