The aim of the paper is to obtain confidence intervals for the tail index and high quantiles taking into account the optimal rate of convergence of the estimator. The common approach to obtaining confidence intervals presented in the literature is to use the normal distribution approximation at...

Estimators of regression coefficients are known to be asymptotically normally distributed, provided certain regularity conditions are satisfied. In small samples and if the noise is not normally distributed, this can be a poor guide to the quality of the estimators. The paper addresses this...

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...