On the Estimation of the Second Order Parameter for Heavy-Tailed Distributions
The extreme-value index γ is an important parameter in extreme-value theory since it controls the first order behavior of the distribution tail. In the literature, numerous estimators of this parameter have been proposed especially in the case of heavy-tailed distributions, which is the situation c...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2013-11-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/138 |
| _version_ | 1828357010721079296 |
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| author | El hadji Deme Laurent Gardes Stéphane Girard |
| author_facet | El hadji Deme Laurent Gardes Stéphane Girard |
| author_sort | El hadji Deme |
| collection | DOAJ |
| description |
The extreme-value index γ is an important parameter in extreme-value theory since it controls the first order behavior of the distribution tail. In the literature, numerous estimators of this parameter have been proposed especially in the case of heavy-tailed distributions, which is the situation considered here. Most of these estimators depend on the k largest observations of the underlying sample. Their bias is controlled by the second order parameter ρ. In order to reduce the bias of γ’s estimators or to select the best number k of observations to use, the knowledge of ρ is essential. In this paper, we propose a simple approach to estimate the second order parameter ρ leading to both existing and new estimators. We establish a general result that can be used to easily prove the asymptotic normality of a large number of estimators proposed in the literature or to compare different estimators within a given family. Some illustrations on simulations are also provided.
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| first_indexed | 2024-04-14T03:08:21Z |
| format | Article |
| id | doaj.art-7e35444eca92468a87a80f4e8cf60d1e |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T03:08:21Z |
| publishDate | 2013-11-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-7e35444eca92468a87a80f4e8cf60d1e2022-12-22T02:15:40ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712013-11-0111310.57805/revstat.v11i3.138On the Estimation of the Second Order Parameter for Heavy-Tailed DistributionsEl hadji Deme 0Laurent Gardes 1Stéphane Girard 2Université Gaston BergerUniversité de Strasbourg INRIA Rhône-Alpes The extreme-value index γ is an important parameter in extreme-value theory since it controls the first order behavior of the distribution tail. In the literature, numerous estimators of this parameter have been proposed especially in the case of heavy-tailed distributions, which is the situation considered here. Most of these estimators depend on the k largest observations of the underlying sample. Their bias is controlled by the second order parameter ρ. In order to reduce the bias of γ’s estimators or to select the best number k of observations to use, the knowledge of ρ is essential. In this paper, we propose a simple approach to estimate the second order parameter ρ leading to both existing and new estimators. We establish a general result that can be used to easily prove the asymptotic normality of a large number of estimators proposed in the literature or to compare different estimators within a given family. Some illustrations on simulations are also provided. https://revstat.ine.pt/index.php/REVSTAT/article/view/138extreme-value theoryheavy-tailed distributionextreme-value indexsecond order parameterasymptotic properties |
| spellingShingle | El hadji Deme Laurent Gardes Stéphane Girard On the Estimation of the Second Order Parameter for Heavy-Tailed Distributions Revstat Statistical Journal extreme-value theory heavy-tailed distribution extreme-value index second order parameter asymptotic properties |
| title | On the Estimation of the Second Order Parameter for Heavy-Tailed Distributions |
| title_full | On the Estimation of the Second Order Parameter for Heavy-Tailed Distributions |
| title_fullStr | On the Estimation of the Second Order Parameter for Heavy-Tailed Distributions |
| title_full_unstemmed | On the Estimation of the Second Order Parameter for Heavy-Tailed Distributions |
| title_short | On the Estimation of the Second Order Parameter for Heavy-Tailed Distributions |
| title_sort | on the estimation of the second order parameter for heavy tailed distributions |
| topic | extreme-value theory heavy-tailed distribution extreme-value index second order parameter asymptotic properties |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/138 |
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