Improvements in the Estimation of a Heavy Tail
In this paper, and in a context of regularly varying tails, we suggest new tail index estimators, which provide interesting alternatives to the classical Hill estimator of the tail index γ. They incorporate some extra knowledge on the pattern of scaled top order statistics and seem to work generall...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2006-06-01
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| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/29 |
| _version_ | 1817999411207208960 |
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| author | Orlando Oliveira M. Ivette Gomes M. Isabel Fraga Alves |
| author_facet | Orlando Oliveira M. Ivette Gomes M. Isabel Fraga Alves |
| author_sort | Orlando Oliveira |
| collection | DOAJ |
| description |
In this paper, and in a context of regularly varying tails, we suggest new tail index estimators, which provide interesting alternatives to the classical Hill estimator of the tail index γ. They incorporate some extra knowledge on the pattern of scaled top order statistics and seem to work generally pretty well in a semi-parametric context, even for cases where a second order condition does not hold or we are outside Hall’s class of models. We shall give particular emphasis to a class of statistics dependent on a tuning parameter τ , which is merely a change in the scale of our data, from X to X/τ . Such a statistic is non-invariant both for changes in location and in scale, but compares favourably with the Hill estimator for a class of models where it is not easy to find competitors to this classic tail index estimator. We thus advance with a slight “controversial” argument: it is always possible to take advantage from a non-invariant estimator, playing with particular tuning parameters — either a change in the location or in the scale of our data —, improving then the overall performance of the classical estimators of extreme events parameters.
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| first_indexed | 2024-04-14T03:08:29Z |
| format | Article |
| id | doaj.art-989f9963210c42a78bc2271a25e8108f |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T03:08:29Z |
| publishDate | 2006-06-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-989f9963210c42a78bc2271a25e8108f2022-12-22T02:15:40ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712006-06-014210.57805/revstat.v4i2.29Improvements in the Estimation of a Heavy TailOrlando Oliveira 0M. Ivette Gomes 1M. Isabel Fraga Alves 2University of LisbonUniversity of LisbonUniversity of Lisbon In this paper, and in a context of regularly varying tails, we suggest new tail index estimators, which provide interesting alternatives to the classical Hill estimator of the tail index γ. They incorporate some extra knowledge on the pattern of scaled top order statistics and seem to work generally pretty well in a semi-parametric context, even for cases where a second order condition does not hold or we are outside Hall’s class of models. We shall give particular emphasis to a class of statistics dependent on a tuning parameter τ , which is merely a change in the scale of our data, from X to X/τ . Such a statistic is non-invariant both for changes in location and in scale, but compares favourably with the Hill estimator for a class of models where it is not easy to find competitors to this classic tail index estimator. We thus advance with a slight “controversial” argument: it is always possible to take advantage from a non-invariant estimator, playing with particular tuning parameters — either a change in the location or in the scale of our data —, improving then the overall performance of the classical estimators of extreme events parameters. https://revstat.ine.pt/index.php/REVSTAT/article/view/29statistics of extremessemi-parametric estimationMonte Carlo methods |
| spellingShingle | Orlando Oliveira M. Ivette Gomes M. Isabel Fraga Alves Improvements in the Estimation of a Heavy Tail Revstat Statistical Journal statistics of extremes semi-parametric estimation Monte Carlo methods |
| title | Improvements in the Estimation of a Heavy Tail |
| title_full | Improvements in the Estimation of a Heavy Tail |
| title_fullStr | Improvements in the Estimation of a Heavy Tail |
| title_full_unstemmed | Improvements in the Estimation of a Heavy Tail |
| title_short | Improvements in the Estimation of a Heavy Tail |
| title_sort | improvements in the estimation of a heavy tail |
| topic | statistics of extremes semi-parametric estimation Monte Carlo methods |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/29 |
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