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| Título | Semi-parametric second-order reduced-bias high quantile estimation |
| Publication Type | Unpublished |
| Year of Publication | 2007 |
| Authors | Caeiro F, Gomes IM |
| Series Title | Preprint |
| Abstract | In many areas of application, like for instance Climatology, Hydrology, Insurance, Finance and Statistical Quality Control, a typical requirement is to estimate a high quantile of probability 1−p, a value, high enough, so that the chance of an exceedance of that value is equal to p, small. The semi-parametric estimation of high quantiles depends not only on the estimation of the tail index γ1, the primary parameter of extreme events, but also on the adequate estimation of a scale first order parameter, C. Recently, apart from new classes of reduced-bias estimators for γ> 0, new classes of the scale parameter C have been introduced in the literature. In all those classes, the second order parameters in the bias are estimated at a level k1 of a larger order than that of the level k at which we compute the tail index estimators. The use of one of those classes of C-estimators in quantile estimation enables us to introduce new classes of high quantiles’ estimators. The asymptotic distributional properties of the proposed classes of estimators are derived and the estimators are compared with alternative ones, not only asymptotically, but also for finite samples through Monte Carlo techniques. An application to the log-exchange rates of the Euro against the Sterling Pound is also provided. |
| URL | http://www.dm.fct.unl.pt/sites/www.dm.fct.unl.pt/files/preprints/2007/8_07.pdf |