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We show that the full-sample bootstrap is asymptotically valid forconstructing confidence intervals for high-quantiles, tail probabilities, andother tail parameters of a univariate distribution. This resolves the doubtsthat have been raised about the validity of such bootstrap methods. In ourextensive simulation study, the overall performance of the bootstrap method wasbetter than that of the standard asymptotic method, indicating that thebootstrap method is at least as good, if not better than, the asymptotic methodfor inference. This paper also lays the foundation for developing bootstrapmethods for inference about tail events in multivariate statistics; this isparticularly important because some of the non-bootstrap methods are complex.

Consistency of full-sample bootstrap for estimating high-quantile, tail probability, and tail index