Minimum-Variance Reduced-Bias Tail Index and High Quantile Estimation
Heavy tailed-models are quite useful in many fields, like insurance, finance, telecommunications, internet traffic, among others, and it is often necessary to estimate a high quantile, i.e., a value that is exceeded with a probability p, small. The semiparametric estimation of this parameter relies...
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| Format: | Article |
| Language: | English |
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Instituto Nacional de Estatística | Statistics Portugal
2008-03-01
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| Series: | Revstat Statistical Journal |
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| Online Access: | https://revstat.ine.pt/index.php/REVSTAT/article/view/54 |
| _version_ | 1817997054704615424 |
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| author | Frederico Caeiro M. Ivette Gomes |
| author_facet | Frederico Caeiro M. Ivette Gomes |
| author_sort | Frederico Caeiro |
| collection | DOAJ |
| description |
Heavy tailed-models are quite useful in many fields, like insurance, finance, telecommunications, internet traffic, among others, and it is often necessary to estimate a high quantile, i.e., a value that is exceeded with a probability p, small. The semiparametric estimation of this parameter relies essentially on the estimation of the tail index, the primary parameter in statistics of extremes. Classical semi-parametric estimators of extreme parameters show usually a severe bias and are known to be very sensitive to the number k of top order statistics used in the estimation. For k small they have a high variance, and for large k a high bias. Recently, new second-order “shape” and “scale” estimators allowed the development of second-order reduced-bias estimators, which are much less sensitive to the choice of k. Here we shall study, under a third order framework, minimum-variance reduced-bias (MVRB) tail index estimators, recently introduced in the literature, and dependent on an adequate estimation of second order parameters. The improvement comes from the asymptotic variance, which is kept equal to the asymptotic variance of the classical Hill estimator, provided that we estimate the second order parameters at a level of a larger order than the level used for the estimation of the first order parameter. The use of those MVRB tail index estimators enables us to introduce new classes of reduced-bias high quantile estimators. These new classes are compared among themselves and with previous ones through the use of a small-scale Monte Carlo simulation.
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| first_indexed | 2024-04-14T02:32:17Z |
| format | Article |
| id | doaj.art-9986c61c63c84b9d933be3f7d0a24d5a |
| institution | Directory Open Access Journal |
| issn | 1645-6726 2183-0371 |
| language | English |
| last_indexed | 2024-04-14T02:32:17Z |
| publishDate | 2008-03-01 |
| publisher | Instituto Nacional de Estatística | Statistics Portugal |
| record_format | Article |
| series | Revstat Statistical Journal |
| spelling | doaj.art-9986c61c63c84b9d933be3f7d0a24d5a2022-12-22T02:17:38ZengInstituto Nacional de Estatística | Statistics PortugalRevstat Statistical Journal1645-67262183-03712008-03-016110.57805/revstat.v6i1.54Minimum-Variance Reduced-Bias Tail Index and High Quantile EstimationFrederico Caeiro 0M. Ivette Gomes 1Universidade Nova de LisboaUniversidade de Lisboa Heavy tailed-models are quite useful in many fields, like insurance, finance, telecommunications, internet traffic, among others, and it is often necessary to estimate a high quantile, i.e., a value that is exceeded with a probability p, small. The semiparametric estimation of this parameter relies essentially on the estimation of the tail index, the primary parameter in statistics of extremes. Classical semi-parametric estimators of extreme parameters show usually a severe bias and are known to be very sensitive to the number k of top order statistics used in the estimation. For k small they have a high variance, and for large k a high bias. Recently, new second-order “shape” and “scale” estimators allowed the development of second-order reduced-bias estimators, which are much less sensitive to the choice of k. Here we shall study, under a third order framework, minimum-variance reduced-bias (MVRB) tail index estimators, recently introduced in the literature, and dependent on an adequate estimation of second order parameters. The improvement comes from the asymptotic variance, which is kept equal to the asymptotic variance of the classical Hill estimator, provided that we estimate the second order parameters at a level of a larger order than the level used for the estimation of the first order parameter. The use of those MVRB tail index estimators enables us to introduce new classes of reduced-bias high quantile estimators. These new classes are compared among themselves and with previous ones through the use of a small-scale Monte Carlo simulation. https://revstat.ine.pt/index.php/REVSTAT/article/view/54statistics of extremestail indexhigh quantilessecond-order reduced-bias semiparametric estimationthird order framework |
| spellingShingle | Frederico Caeiro M. Ivette Gomes Minimum-Variance Reduced-Bias Tail Index and High Quantile Estimation Revstat Statistical Journal statistics of extremes tail index high quantiles second-order reduced-bias semiparametric estimation third order framework |
| title | Minimum-Variance Reduced-Bias Tail Index and High Quantile Estimation |
| title_full | Minimum-Variance Reduced-Bias Tail Index and High Quantile Estimation |
| title_fullStr | Minimum-Variance Reduced-Bias Tail Index and High Quantile Estimation |
| title_full_unstemmed | Minimum-Variance Reduced-Bias Tail Index and High Quantile Estimation |
| title_short | Minimum-Variance Reduced-Bias Tail Index and High Quantile Estimation |
| title_sort | minimum variance reduced bias tail index and high quantile estimation |
| topic | statistics of extremes tail index high quantiles second-order reduced-bias semiparametric estimation third order framework |
| url | https://revstat.ine.pt/index.php/REVSTAT/article/view/54 |
| work_keys_str_mv | AT fredericocaeiro minimumvariancereducedbiastailindexandhighquantileestimation AT mivettegomes minimumvariancereducedbiastailindexandhighquantileestimation |