Tail index estimation depends for its accuracy on a precise choice of the sample fraction, i.e. the number of extreme order statistics on which the estimation is based. A complete solution to the sample fraction selection is given by means of a two step subsample bootstrap method. This method...

Estimators of the extreme-value index are based on a set of upper order statistics. We present an adaptive method to choose the number of order statistics involved in an optimal way, balancing variance and bias components. Recently this has been achieved for the similar but somewhat less...

For samples of random variables with a regularly varying tail estimating the tail index has received much attention recently. For the proof of asymptotic normality of the tail index estimator second order regular variation is needed. In this paper we first supplement earlier results on...

We characterize second order regular variation of the tail sum of F together with a balance condition on the tails interms of the behaviour of the characteristic function near zero.

For testing whether a distribution function is heavy tailed, we study the Kolmogorov test, Berk-Jones test, score test and their integrated versions. A comparison is conducted via Bahadur efficiency and simulations. The score test and the integrated score test show the best performance. Although...