Peaks Over Random Threshold Methodology for Tail Index and High Quantile Estimation
In this paper we present a class of semi-parametric high quantile estimators which enjoy a desirable property in the presence of linear transformations of the data. Such a feature is in accordance with the empirical counterpart of the theoretical linearity of a quantile χp: χp(δX + λ) = δχp(X) + λ,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2006-11-01
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| Series: | Revstat Statistical Journal |
| Subjects: | |
| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/37 |
| _version_ | 1818513156041867264 |
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| author | Paulo Araújo Santos M. Isabel Fraga Alves M. Ivette Gomes |
| author_facet | Paulo Araújo Santos M. Isabel Fraga Alves M. Ivette Gomes |
| author_sort | Paulo Araújo Santos |
| collection | DOAJ |
| description |
In this paper we present a class of semi-parametric high quantile estimators which enjoy a desirable property in the presence of linear transformations of the data. Such a feature is in accordance with the empirical counterpart of the theoretical linearity of a quantile χp: χp(δX + λ) = δχp(X) + λ, for any real λ and positive δ. This class of estimators is based on the sample of excesses over a random threshold, originating what we denominate PORT (Peaks Over Random Threshold) methodology. We prove consistency and asymptotic normality of two high quantile estimators in this class, associated with the PORT-estimators for the tail index. The exact performance of the new tail index and quantile PORT-estimators is compared with the original semiparametric estimators, through a simulation study.
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| first_indexed | 2024-12-10T23:57:16Z |
| format | Article |
| id | doaj.art-9705a3c9c935483a979fbe9df8a758cb |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-12-10T23:57:16Z |
| publishDate | 2006-11-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-9705a3c9c935483a979fbe9df8a758cb2022-12-22T01:28:34ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712006-11-014310.57805/revstat.v4i3.37Peaks Over Random Threshold Methodology for Tail Index and High Quantile EstimationPaulo Araújo Santos 0M. Isabel Fraga Alves 1M. Ivette Gomes 2Instituto Politécnico de SantarémUniversidade de LisboaUniversidade de Lisboa In this paper we present a class of semi-parametric high quantile estimators which enjoy a desirable property in the presence of linear transformations of the data. Such a feature is in accordance with the empirical counterpart of the theoretical linearity of a quantile χp: χp(δX + λ) = δχp(X) + λ, for any real λ and positive δ. This class of estimators is based on the sample of excesses over a random threshold, originating what we denominate PORT (Peaks Over Random Threshold) methodology. We prove consistency and asymptotic normality of two high quantile estimators in this class, associated with the PORT-estimators for the tail index. The exact performance of the new tail index and quantile PORT-estimators is compared with the original semiparametric estimators, through a simulation study. https://revstat.ine.pt/index.php/REVSTAT/article/view/37heavy tailshigh quantilessemi-parametric estimationlinear propertysample of excesses |
| spellingShingle | Paulo Araújo Santos M. Isabel Fraga Alves M. Ivette Gomes Peaks Over Random Threshold Methodology for Tail Index and High Quantile Estimation Revstat Statistical Journal heavy tails high quantiles semi-parametric estimation linear property sample of excesses |
| title | Peaks Over Random Threshold Methodology for Tail Index and High Quantile Estimation |
| title_full | Peaks Over Random Threshold Methodology for Tail Index and High Quantile Estimation |
| title_fullStr | Peaks Over Random Threshold Methodology for Tail Index and High Quantile Estimation |
| title_full_unstemmed | Peaks Over Random Threshold Methodology for Tail Index and High Quantile Estimation |
| title_short | Peaks Over Random Threshold Methodology for Tail Index and High Quantile Estimation |
| title_sort | peaks over random threshold methodology for tail index and high quantile estimation |
| topic | heavy tails high quantiles semi-parametric estimation linear property sample of excesses |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/37 |
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