Economic problems such as large claims analysis in insurance and value-at-risk in finance, requireassessment of the probability P of extreme realizations Q. This paper provided a semi-parametricmethod for estimation of extreme (P, Q) combinations for data with heavy tails. We solve the...

We use a subsample bootstrap method to get a consistent estimate of the asymptotically optimal choice of the samplefraction, in the sense of minimal mean squared error, which is needed for tail index estimation. Unlike previous methodsour procedure is fully self contained. In particular, the...

The selection of upper order statistics in tail estimation is notoriously difficult. Most methods are based on asymptotic arguments, like minimizing the asymptotic mse, that do not perform well in finite samples. Here we advance a data driven method that minimizes the maximum distance between...