Generalized Sum Plots
Sousa and Michailidis (2004) developed the sum plot based on the Hill (1975) estimator as a diagnostic tool for selecting the optimal k when the distribution is heavy tailed. We generalize their method to any consistent estimator with any tail type (heavy, normal and light tail). We illustrate the...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2011-10-01
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| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/103 |
| _version_ | 1798036661592915968 |
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| author | J. Beirlant E. Boniphace G. Dierckx |
| author_facet | J. Beirlant E. Boniphace G. Dierckx |
| author_sort | J. Beirlant |
| collection | DOAJ |
| description |
Sousa and Michailidis (2004) developed the sum plot based on the Hill (1975) estimator as a diagnostic tool for selecting the optimal k when the distribution is heavy tailed. We generalize their method to any consistent estimator with any tail type (heavy, normal and light tail). We illustrate the method associated to the generalized Hill estimator and the moment estimator. As an attempt to reduce the bias of the generalized Hill estimator, we propose new estimators based on the regression model which are based on the estimates of the generalized Hill estimator. Here weighted least squares and weighted trimmed least squares is proposed. The bias and the mean squared error (MSE) of the estimators is studied using a simulation study. A few practical examples are proposed.
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| first_indexed | 2024-04-11T21:15:58Z |
| format | Article |
| id | doaj.art-a3f9e5d5b3894f0486c0b2d2189f4803 |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-11T21:15:58Z |
| publishDate | 2011-10-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-a3f9e5d5b3894f0486c0b2d2189f48032022-12-22T04:02:49ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712011-10-019210.57805/revstat.v9i2.103Generalized Sum PlotsJ. Beirlant 0E. Boniphace 1G. Dierckx 2Katholieke Universiteit LeuvenKatholieke Universiteit LeuvenHogeschool-Universiteit Brussel Sousa and Michailidis (2004) developed the sum plot based on the Hill (1975) estimator as a diagnostic tool for selecting the optimal k when the distribution is heavy tailed. We generalize their method to any consistent estimator with any tail type (heavy, normal and light tail). We illustrate the method associated to the generalized Hill estimator and the moment estimator. As an attempt to reduce the bias of the generalized Hill estimator, we propose new estimators based on the regression model which are based on the estimates of the generalized Hill estimator. Here weighted least squares and weighted trimmed least squares is proposed. The bias and the mean squared error (MSE) of the estimators is studied using a simulation study. A few practical examples are proposed. https://revstat.ine.pt/index.php/REVSTAT/article/view/103sum plotgeneralized sum plotextreme value analysisgeneralized quantile plotweighted regression model |
| spellingShingle | J. Beirlant E. Boniphace G. Dierckx Generalized Sum Plots Revstat Statistical Journal sum plot generalized sum plot extreme value analysis generalized quantile plot weighted regression model |
| title | Generalized Sum Plots |
| title_full | Generalized Sum Plots |
| title_fullStr | Generalized Sum Plots |
| title_full_unstemmed | Generalized Sum Plots |
| title_short | Generalized Sum Plots |
| title_sort | generalized sum plots |
| topic | sum plot generalized sum plot extreme value analysis generalized quantile plot weighted regression model |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/103 |
| work_keys_str_mv | AT jbeirlant generalizedsumplots AT eboniphace generalizedsumplots AT gdierckx generalizedsumplots |