Direct Reduction of Bias of the Classical Hill Estimator
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 compute...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2005-11-01
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| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/21 |
| _version_ | 1828354830231404544 |
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| author | Frederico Caeiro M. Ivette Gomes Dinis Pestana |
| author_facet | Frederico Caeiro M. Ivette Gomes Dinis Pestana |
| author_sort | Frederico Caeiro |
| collection | DOAJ |
| description |
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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| first_indexed | 2024-04-14T02:32:12Z |
| format | Article |
| id | doaj.art-8b3c8758ce014f5abe45a32f04d8c0b4 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T02:32:12Z |
| publishDate | 2005-11-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-8b3c8758ce014f5abe45a32f04d8c0b42022-12-22T02:17:39ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712005-11-013210.57805/revstat.v3i2.21Direct Reduction of Bias of the Classical Hill Estimator Frederico Caeiro 0M. Ivette Gomes 1Dinis Pestana 2Universidade Nova de LisboaUniversidade de LisboaUniversidade de Lisboa 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. https://revstat.ine.pt/index.php/REVSTAT/article/view/21statistics of Extremessemi-parametric estimationbias estimationheavy tails |
| spellingShingle | Frederico Caeiro M. Ivette Gomes Dinis Pestana Direct Reduction of Bias of the Classical Hill Estimator Revstat Statistical Journal statistics of Extremes semi-parametric estimation bias estimation heavy tails |
| title | Direct Reduction of Bias of the Classical Hill Estimator |
| title_full | Direct Reduction of Bias of the Classical Hill Estimator |
| title_fullStr | Direct Reduction of Bias of the Classical Hill Estimator |
| title_full_unstemmed | Direct Reduction of Bias of the Classical Hill Estimator |
| title_short | Direct Reduction of Bias of the Classical Hill Estimator |
| title_sort | direct reduction of bias of the classical hill estimator |
| topic | statistics of Extremes semi-parametric estimation bias estimation heavy tails |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/21 |
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