Semi-parametric second-order reduced-bias high quantile estimation

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 or extreme value index gamma, the primary parameter of extreme events, but also on the adequate estimation of a scale first order parameter. Recently, apart from new classes of reduced-bias estimators for gamma > 0, new classes of the scale first order parameter have been introduced in the literature. Their use in quantile estimation enables us to introduce new classes of asymptotically unbiased high quantiles' estimators, with the same asymptotic variance as the (biased) "classical" estimator. 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.